Hi there, welcome back to Gamedev Academy. I'm Shane. Please let me know you're here by leaving a comment down below Just like these fine human beings did in the last one and remember to let me know Which house you're in if you've joined us on discord. In the last class We made it so that when a new ball is spawned it will follow the paddle until it is shot into the level and Now in this class what we're going to be doing is making it so that we can shoot the ball off into the level So without any further messing about let's get stuck in Now that we've got the ball following the paddle at the beginning of the game What we need to do now is get get it so that the player can shoot the ball into the game themselves So previously we had it that the ball would just fly off into the level at the beginning of the game We don't want that we want to give that ability to the player. So let's get that set up Shall we so the first place I want to go is into the ball blueprint. So let's get that bad boy open Here it is and I want to update this launch ball event So if you remember we set an active property an active variable on the ball And we need to know at times whether or not this is active or not when the ball is launched into the level That means the ball is active and that's going to stop us being able to spawn a new ball So just into this launch ball event what I need to do And just move this along here is out of launch ball. We're going to set set Active and we're going to set that to true and then we'll know that the ball is in play So we'll compile that and while I'm in this blueprint I also want to we set this up here, which is to get the player controller. So I'm just going to comment this as well get player controller Or just get play will be fine. I say that's so just so I know that I'm casting to it there If I ever forget which is likely and we no longer need to launch ball here so I'm going to get rid of that as well and That because we're going to handle that elsewhere So we'll just now move these over here. Just to keep things lined up a little bit Okay, so I'm done in this blueprint. Let's compile that I'll save it as well and Then what I want to do now is going to the player paddle blueprint And this is where we're going to set up the ball launching So we need this action to be triggered by an event which is going to be when the player presses the fire key so if we go to the Project settings hopefully you'll remember that we set up an input right at the beginning For fire, that's what it's called and w up or space bar will cause the ball to be fired So we can now go into our player paddle right click and if we just type fire because that's what we called it We get an event for that beautiful So this is going to happen when we press that key or one of those three keys So what we need to do first of all is get some information about the ball And we've got a ball variable here Which if you remember when we spawned the actor the ball we set that into a variable So every new ball that comes in that spawned what we can do is then mess about with it So we're going to get the ball And we need to know a few bits about it first of all we need to know is it valid So we're going to do is valid and we're going to use the one with the F next to it Now we go and what that tells us is whether or not the ball exists So if the ball doesn't exist if it's not spawned for some reason then we can't launch it So that's one thing that we need to know did the ball spawn properly is actually there We also need to know Is it active So we're going to get active Because if it's been launched into the game and it is active we don't want this to work So only if it's not active so moving forward from here then this actually needs to have a not coming out of it And not boolean because we're only going to work with this if active is not true So there's the not there and we need both of these So not active and is it valid if both of those are true we can move on so we're going to add an and boolean To get those two to work together. So plug those in So there you go if the ball is valid and if it's not active we can move on What we've set up here is a condition So we're going to just come out of here and we're going to do a branch. There we go. So when we press Fire The first thing we're going to do is ask these questions is this is the condition before we can move any further So is it valid and is it not active and if that is true we can move forward And so what I'm going to do I could just use this ball reference here But that's going to get a bit messy So I'm going to get a new reference just to bring it a bit closer get ball and then out of here I'm going to go launch And that relates to the custom event launch ball that we have in here this one there it's going to add the impulse to it and set the ball to active and That's going to happen on true So what we're saying is We press fire Ask these questions if it comes back true perform launch ball on the ball So we can now compile that and Now would be a good time to test whether or not this is working. So let's go here We'll press play I'll click here to make it active So I can still move left and right which is a good sign the ball at this stage is still following the paddle And if I press I'm going to press up on my keyboard and it fires So we've managed to get that functionality working perfectly So now what's going to happen is I'm going to let the ball go and this creates a problem because there's nothing Killing that ball when it falls out of the play area So we can't use anything to trigger the spawning of a new ball to keep the game rolling So moving forward in the next step what we need to do is get that functionality in place So what we're going to do first of all is put a kill zone in something to kill the ball When it goes out of the play space, but just to tidy things up before we move on. Let's comment this So put it on in there press C and I'm going to call this launch Fireball I think fireball There we go. That's lovely. I'm gonna line that up Okay, so that's that step finished I will see you in the next step where we will be able to kill some balls. I believe that quality education should be available to everybody and for that reason all of the classes at Game Dev Academy are Completely free and we're supported by our very generous school governors over at patreon If you'd like to become a Game Dev Academy governor and support our work as well as helping us to steer the channel in The right direction then use the link in the description to be taken to the patreon page


Okay, so let me demonstrate something here. Now, I have to be very careful because as it turns out, these stands are magnetized, which I didn't appreciate the first time I did this. So I have here, let me do this. This up here, terrifying. Okay, I'm gonna just take this camera, and the camera is primarily made of plastic, non-conductive, non-magnetizable material. All right, so I have here a compass, all right? And we'll try moving it here. All right, so if I let that settle for a second, you'll see that it points in the direction that north is supposed to be. So let me line up N on the compass roughly if I can. Okay, so now we know which way is east and south and west and so forth, okay? So there we go and get the reflection off this.  Okay, a little easier to see now. Okay, so I have this assembly here now with a coil of wire, that's the orange stuff. So it's just wire that's been looped many times around a piece of plastic, and it's coated with a thin plastic coating so that the wire doesn't actually come in electrical contact with itself. So those loops are actually electrically isolated from one another by just a thin little clear plastic coating. This is a very common way of making coils of wire like this. If you didn't do this, then you short the loop. So the current would not flow through each cycle of the loop, it would just run the shortest path to the other end and come back to the power source. Okay, so I have a switch here, all right? And I have power coming in from this low-voltage power supply over here on the right. So it's plugged in, and at this point I can switch this on. You should see a green light come on. Now, I'm only gonna get to do this experiment a couple of times, so I need you to watch very carefully, all right? So we have here again, the compass still pointing north, loop of wire over here, and I'm gonna throw the switch, watch the compass. All I'm doing is running an electric current through the loop of wire. There are no magnets anywhere else near this. There's no magnets in my hand, okay? All I have to do is close the switch and make a current flow, and I can change the direction of north locally. This in and of itself was an astounding discovery. For almost 2,000 years, human beings have been playing around with magnets, not at all understanding where magnetic fields came from. They seemed to be something apart as chemists and physicists and mathematicians started studying the electric phenomenon. The magnetic phenomenon seemed eerily similar. In fact, there were scientists that suspected a connection between the electric phenomenon and the magnetic phenomenon, but no one could quite prove it until one day, quite fortuitously, while doing a lecture demonstration for his students in a physics class, Hans Christian Ursted closed the switch on a battery and noticed that a very thin metal compass needle deflected nearby, and he did it again, and the compass needle deflected again, and it was a eureka moment for him, because he realized it's not static electric charge. I mean, I could put, for instance, that device I showed you at the beginning of class that can hold charge. I could, for instance, I could rub PVC pipe and hold it next to this very still, and this compass won't respond, but if you move charge, it creates a magnetic field that affects permanent magnets. In this case, it made the compass needle deflect. Terrifying, let me get rid of that, okay? So, let me reinforce this a bit. Okay, so, Hans Christian Ursted. Here he is, Danish physicist and chemist. There we go. And, as I said, he observed in 1820 that electric current caused a compass needle to deflect. That was his basic, simple observation of the natural world, and it caused quite a stir when he published his results.  Now, the reason I only get to do this a few times is this is copper wire, this is copper wire. There's not a whole lot of resistance in this circuit. I didn't put a light bulb in here, all right? So, there's a big current of order in amp or two that's flowing through this copper wire straight back into the power supply. I'm effectively shorting the power supply through the circuit. So, eventually, if I leave this on long enough, it's actually warm to the touch now, there's a safety mechanism that when it gets too hot, it pops a little switch, and the power supply doesn't work anymore. If I do that four or five times in a row quickly, I can short the power supply, and it will save itself by breaking the circuit. When it cools down again, I can pop the switch back in. So, I didn't actually get it to flip this time, but I did this while I was practicing the demonstration. It's actually quite difficult to get this to work. You need a lot of current, and so, you know, Ersted needed really strong chemical cells, and he wasn't the one that developed them, other people developed them, and he was using them in experiments. So, and as I said, he actually first observed this amazing phenomenon while doing a lecture demonstration of electricity in front of his students in his class. So, this marks the discovery of what we now call electromagnetism, which is a relationship between electricity, the electric force, and magnetism, the magnetic force, that's intimate and related through the motion of charge. So, what we learn at this point is magnets, okay, like these permanent magnets, will respond to other permanent magnets, like the earth. So, the north will line up with the south magnetic pole of the earth, which is the geographic north pole, okay? We also know that electric charge, okay, we can take a magnet, we can put it in the path of electrons, and they will deflect if their velocity vector is at any angle to the magnetic field from the permanent magnet. Magnets affect electric charge, but we also see a beautiful symmetry here. Electric charge in motion affects magnets. They generate magnetic fields, and this was a stunning revelation at the time, and we have benefited immensely from this very basic observation about the natural world. So, let's watch this. This is awesome stuff, I can see it. This is a magnetic fluid, by the way. Has anyone ever seen this before? Let me go back here. So, magnetic fluids are just like solid permanent magnets except liquid form. And they're neat, because if you spritz them onto a permanent solid magnet, you can see the magnetic field lines. See the dipole field lines shooting out of the top, coming out of the sides.  It was a famous car commercial a couple of years ago, and I first started teaching the course, and it was a car commercial about the fact that this car company uses a magnetic fluid as part of their brake system to create a more responsive brake system. So, that fluid is actually used by car manufacturers to improve the quality of safety systems on a vehicle like Bricks. This is awesome stuff. I can sit here and stare at this for a moment. He's gonna do another demonstration in a moment. And it's similar to what I just did. I used to have to only show the video because I couldn't get enough current to do this, but this year I got it to work. But the standard judicial way of showing magnetic fields is with a compass. I've got a wire. Big-ass wire. I've got it surrounded by compasses. A compass points towards a magnetic field. If you were to bring a strong magnet near it, they would point towards it. It's like a little strong magnet in my hand easy to point towards it. And an interesting phenomena takes place. You get lined up. When we put electricity... So, they're all pointing north. It creates a magnetic field. And then they all start to point around the wire. It's going around that wire. And if you wrap the fingers of your hand, they go in the direction of the magnetic field. You curl your hand around the wire. That's another right hand rule. Like this. Curl the fingers around for your hand around it. The thumb indicates the direction of current. It's got this picture upside down. I don't know why you did that, but... Okay, so we'll come back to that in a minute. But let's just sort of take a look at a photograph of that experiment. Not using compass needles, which are big, but using little iron filings.  A little bar magnet. And if you take a wire and run a couple of amps through it, and in this case they cut a hole in a piece of paper. So non-conductive paper. They ran a conductive wire up perpendicular through the paper. Okay, so out of the plane of the paper. They ran an electric current through the wire. And the iron filings on the paper, which were originally just shaken randomly and uniformly on the paper, they line up. And isn't it, this is gorgeous, right? You can see the current is going up the wire and the magnetic field is circulating around that wire. And it was this observation that two physicists used to now write down a law that we understand deeply predicts the magnetic fields caused by electric currents. Katherine, did you have a question? Yeah, I was wondering why they wouldn't all line up like on top of each other, because wouldn't they want to get as close as possible to the kind? Absolutely. And the paper has friction. So their rotating is pretty easy, you know? But sliding that whole little bit of... So they're just like placed all on there? Well, they're just shaken on the paper and then you kind of just kind of tap the paper to get them to settle uniformly.  And they'll line up along magnetic field lines. So what you're seeing here is the little bar magnets are, each of them is sort of like a little, it's like a little bit of, you're kind of looking at calculus here, but done physically.  So the magnetic fields appear to be in the plane of the paper and they are circulating perpendicular to the current flow. Again, you can't get away from the cross product with magnetic fields. The current goes this way, the magnetic field goes at an angle to that, that's perpendicular. We'll see what B.O. and Savart did in a moment. Used a lot of experiments using compass needles to figure out the form of the rule, okay? But yeah, so I mean, if you waited long enough and there was a less low enough friction that would allow motion in the plane as well. Yeah, eventually those little ferromagnets, the little iron filings would clump closer and closer to the wire. That would be dangerous because you'd start making electrical connections between the wire and iron, which is conductive. And well, eventually you could cause shorts or sparks or things like that. Cause that's again, that's like probably two or three amps of current going through that, that's a lot of current. You know, you don't wanna short that or touch that with your finger. Cause we know what just a few milliamps will do to a human being. So these are they. Actually, I thought it was kind of interesting as I was doing a little bit of historical homework for this slide, that there's a photograph of Jean-Baptiste Bo from 1851 or so, so maybe about a decade before he died. Photography was only commercially available as of about 1839 or so. It'd been invented in the decades prior to that. But in terms of commercial photography, that wasn't really something you could get. You couldn't get a commercial photograph until almost 1840. So, you know, within a decade after commercial photography first appeared, people were photographing other people and there's a picture of a very old Jean-Baptiste Bo. And this is probably closer to when he was doing his work in the what, 18, well, 1820 actually, the year that Ursted published his results was the year that Savard and Bo did their research with compass needles and currents to figure out what the rule was for having a current in some length of wire and then getting some resulting magnetic field from that. They figured out the mathematical relationship for that. So they worked together, you know, in about 1820 and came up with this thing we now call the Bio-Savart Law. So let me show this to you and I'll spend the last five minutes kind of talking a little bit about this, all right? It looks nasty, all right? So dust off your calculus, because here we go. What I'll do in the next lecture is I will show you how to calculate the magnetic field from a straight wire. And if there's time, I'll also do a circle. And then we're gonna do an exercise next week that synthesizes everything that we've been learning about magnetism so far. And those things are magnets cause other magnets to repel or attract, okay? We know that from just playing with magnets. We know from experimenting, I showed you the cathode ray tube, we know that electric charge can be deflected by magnetic field. So magnetic fields affect moving charge. Moving charge generates magnetic fields. That's what the Bio-Savart Law encapsulates. We observe the phenomenon in nature, we describe it mathematically. And it requires calculus. So just like Coulomb's law, this is the Coulomb's law of magnetism. This law tells you that thanks to moving charge, I, Coulomb's per second, you get a magnetic field B resulting from that. And in order to figure out the magnitude and the direction of the field given the current and the length of the conductor, there is a relationship, okay? So the magnetic field, so let's take a look at this bendy wire I have over here. Let's focus on just a little piece of the wire which I'll call DL vector. So DL vector is just a little piece of the length of the wire and the direction that that little vector points is the direction that current I is flowing, okay? So this is current I. Comes in the wire, snakes around, goes out that end over there. I'm only showing you a little piece of it right now. And if we were over at some point P, which I've indicated with the black dot, we would experience a little bit of magnetic field due to that little bit of conductor. Now of course the total magnetic field is the sum of the effects of the current here and here, here, here, here, all the way up there. But if we can calculate using coordinate systems and vectors, one piece of the wire and then we can integrate over the whole wire using some trick, we can get the total magnetic field. We can sum all the little DBs that result from these little IDLs, these little current times these little length vectors in the conductor. Now, we know from experiment, so like the demonstration I did here, it's easier to see in the demonstration in the video or the little paper with the wire going through it and you can see the circles of magnetic field around the wire. We know from that that the direction that the current flows is perpendicular to the direction that the magnetic field points. So if the current points this way, up here the magnetic field might point that way, over here it might point down, it's always perpendicular to the direction of the current flow and that's what gives you a circulating magnetic field around the wire, okay? So that's an empirical observation. That's when you do the experiment, that's what nature does and so mathematics you use to describe that phenomenon and try to figure out the exact precise relationship. So beyond some of our work really hard with little compass needles to do this, they mapped out magnetic fields from wires and they came up with the rule that the magnetic field direction is at right angles to the current flow, which we already knew, but the trick is if you draw a vector from the little piece of wire out to where you're observing the field and you use a right hand rule, okay? DL points that way, R points that way, the magnetic field at point P will point out of the page according to the direction where your thumb is pointing. So again, DL, R, DB, that's what they figured out and the only way you can describe that is with a cross product. You have to know the DL, you have to write down the R and you have to then from that compute the direction of B and the magnitude of B. Now the magnitude of B comes from multiplying IDL and then the unit vector R hat and dividing that whole thing by the distance squared, they found that much like with Coulomb's law, the magnetic field strength seems to decrease as a function of distance and the rule that they worked out is just like Coulomb's law, it's an inverse square law which is already in and of itself fascinating that that happens to be the same. And then it turns out you have to multiply the number you get from this by a constant, mu naught over four pi and mu naught is, well I'll define it next time but it's actually really easy to remember, it's four pi times 10 to the seven. That's it, four pi times 10 to the seven, it has units but we'll talk about this next. There we go, has limiters squared over amps. Okay, so this is another number that you can commit to memory or write on the formula sheet. It has a name, let me just skip to the next slide here, it has a name, epsilon naught which we've seen already in electricity. Okay, so that's related to K, one over four pi epsilon naught is equal to K, that constant we encountered at the beginning of the course. Epsilon naught is actually considered to be the fundamental number, it's the number that physicists talk about when they talk about electricity. And it has a name, it's called the permittivity of free space, I think I've mentioned this before but I'll formally mention it now. It's given its own name, it's so important in electricity that we named it. And from a capacitor, if you remember the field inside of a capacitor, an ideal parallel plate capacitor, it was proportional to epsilon naught, right? It was the area of the plates divided by the separation of the plates times epsilon naught. And so epsilon naught is meant to describe somehow if you have nothing in between the plates, it sort of describes the freedom with which electric fields have to propagate through empty space. And if you add any material into that empty space, if you put a dielectric inside the capacitor, you will weaken the electric field. So you'll change the permittivity of free space to something else by multiplying it by a number of kappa that's one or greater, okay? So this number physically represents what is known as the dielectric properties of empty space. And similarly, mu naught represents the, in a magnetic sense, the dielectric properties of empty space. So mu naught is the equivalent of epsilon naught but for magnetic fields. And it tells us how permeable free space is to magnetic field propagation in the same way that epsilon naught tells us how much empty space permits electric fields to propagate through it. Now this might seem kind of random.  I mean, they're just numbers that some French guys figured out in a lab. So be it. But it turns out that they actually have a deep connection to a much more important number. And I won't talk about it today, but in one of the lectures that you're gonna get in the next couple of weeks, there is going to be a lecture that talks about the nature of light. And what is light exactly before we get into optics? And there isn't gonna be any reading for that lecture.  And it will unite absolutely everything that we'll have talked about up to that point in the course before we get into optics. And optics is just the transportation. Okay, so going back to B.O.Sovar, let's do an exercise with B.O.Sovar, all right? And the exercise that I'm interested in doing is the magnetic field from a long straight wire. Christian, yes? One more question. Yeah, yeah. Are we gonna get our homework back or grade it? Yes, yeah, yeah, yeah. So I, Govind is still working on the homework from last week. I asked him to grade one of two problems, and so he's kind of flipping between those, getting that one. Yeah. Okay. Okay, so let's imagine we have a long, straight, current-carrying wire, all right? So I'm gonna just draw a little section of it, but I want you to imagine that it continues on to infinity in both directions. So let me just say that goes out to plus infinity, and that goes out to minus infinity. I'm really under-representing this wire, okay? So really long, straight wire. So we don't have to worry about what's going on at the ends. Very far away from us. And we're up here at this point, P, and we're going to try to calculate the magnetic field at that point. So far, this is looking a whole lot, like Coulomb's law of trying to figure out the electric field from a long line of charge with some charge density lambda. Well, there's no lambda anymore for this. There's just current, I, constant current. So in place of linear charge density for this problem, we'll have I to deal with, okay? In place of dQ, okay? In place of dQ, we have to deal with dL vector, the little piece of the wire where the direction of dL vector points in the direction of the current. All right, so let's go ahead and pick a little piece of the wire, I'll shade it in here, okay? So this right here is our little so-called current element, current element, I dL vector. Yeah, I haven't done anything with coordinate systems yet, I'm just labeling pieces using B of sub R.  And we have one more vector to write, so actually, let's write the vector here. So as I said, we have to say where the current is going, so let's say current is going to the right. And actually, in anticipation of using Cartesian coordinates, let me make a quick little notation change here, and let me switch this to big I. So we have a current big I going to the right, because I'm gonna need I hats and J hats and I hats. Okay, and then finally, just like with Coulomb's law problems, the R vector, where does that go from and to? Well, it goes from the thing creating the magnetic field to the place where we're measuring the magnetic field. So it goes from the current element to the point P. But that convention remains exactly the same as before. Okay, we're missing a coordinate system here. We need to start writing things down in terms of stuff we can actually maybe later integrate, for instance, okay? So we need some coordinates. And I'm going to choose to put my observation point right on the Y axis. And I'm going to choose my wire to lie along the X axis. So positive I hat is to the right. Positive J hat is up. And again, using this little right hand rule, X, Y, Z, Z points out of the board. So let me just go ahead and draw. There's the Z, the Z axis points out of the board like that at a 90 degree angle to both X and Y. The classic Cartesian coordinate system. All right, angles. Okay, well, we can already basically use the right hand rule for a cross product to anticipate where this magnetic field DB vector is going to have to point from this current element. So for instance, we can take our index finger, we can point it in the direction of DL vector, which points in the direction of the current. I can then point my index finger in the direction of our hat, which is the direction that our vector points in. So I'm actually already doing that. And then my thumb indicates the direction of the magnetic field. The little piece of magnetic field DB vector will point in this picture. So without doing any calculations, I can already create a situation that I can use to cross check my answer later. I expect that little piece of magnetic field that when I write it down, I expect it to point out in the positive Z direction, the K hat direction. So let's just mark that for later. It appears that DB vector will be written as something like a magnitude times K hat. We don't know what DB is yet. We've gotta write that in terms of I and L and R and hopefully some Cartesian coordinates in there someplace, okay? We'll try to rewrite this in terms of our coordinate system. But we can anticipate that that's what we expect to see. All right, something that points in the K hat direction, something that points along the Z axis. And that makes sense because the Beaus of Art law says that the magnetic field element from that current element had better point perpendicular to both DL and R hat. And since DL is in the plane of the blackboard and R is in the plane of the blackboard, the only place where you can be at right angles to both of those is either out of the plane or into the plane. So perpendicular to the plane like this, okay? So let's just, let's file that away for a second and let's do some math. Just like Coulomb's law, we now seek to represent R, R hat, R vector, DL in terms of coordinates. So let's do IDL first, okay? IDL vector. Well, a couple of things we notice. First of all, this is supposed to point in the direction that the current is pointing. And what direction is the current pointing by construction in my coordinate system? S, yeah. So it's pointing in the positive I hat direction. In fact, any current element I look at in here, the current element vector will always point along I hat. So I can write this one, for instance, as IDL I hat. So I've got the direction all taken care of in terms of my coordinate system. That's done. DL, all right, well what is this? This is a little piece of the length of this wire which goes out to positive infinity that way and negative infinity that way.  So DL can be identified merely as DX. And if I were to look at another piece of this, it would be a DX over here or maybe a DX over here or over here. But they're all little DXs. They're all pieces of the x-axis for this conductor. So that's about as far as I can go. I mean, I would assume in a problem like this that you'd be given the current. Okay, so you'd be given a number for I. Now DX is something we can integrate. You can imagine that our integral, when we sum up all the little current elements to get the magnetic field, we're gonna be summing over DXs. And DXs are gonna go from negative infinity to positive infinity. So we already have our limits of integration figured out too. Let's move on to R. Okay, so R vector, well, our vector is the vector that we have to take. We're gonna break it into Cartesian components, x's and y's and z's as needed, okay? It's the path that we wanna take to go from the current element to P, all right? Along our axes. So to go from our current element at some distance x out from the origin of the coordinate system back to the origin. And then from the origin up to P, okay? Which we'll write as being some distance D above the line. So we're some distance D above the line in this. It's actually not too bad. We have to go a distance x in the negative i hat direction. And then we have to go a distance D in the positive j hat direction. And that's our R vector in terms of our coordinate systems. Okay, x, well, x is the thing we're gonna integrate over later. So that's good. We've got x in here. D is just a constant. We're just at a fixed height above the wire. In fact, no matter which current element you pick anywhere on this wire, it'll always be this height D above the line. Okay, that shortest distance from the wire to the point P is always D. So D never changes for any of the current elements. X changes, but D doesn't. And we're gonna integrate over x, so that's good news. And then, great, so magnitude of R is just going to be, well, R squared is gonna be x squared plus D squared. Okay, that's easy enough to do from Pythagorean theorem or you can square, you can take the dot product of R vector with itself to get R squared, whatever you like. But Pythagorean theorem works just fine for this. It's a right triangle. So you wanna get the length of the hypotenuse you take x squared plus D squared. That's the hypotenuse length squared. Done. Yeah? I guess rewriting terms you're not using the formulas. I haven't like, yeah, I'm just getting things into coordinates. Yeah, using my coordinate system, which is usually the longest step. Getting things into the coordinates. Outline and then we'll use the formulas. And then we'll get this into an integral. Okay. And then we'll integrate it, right? All right, so finally we have R half. Well, that's just R vector divided by its length. And we already have R vector and we already have the length. So we just have to write an ugly looking ratio here. So this is going to be negative x i hat plus D j hat all over the, I'll write it this way, x squared plus D squared to the one half power or the square root of x squared plus D squared. That's what R is. It's the square root of this equation. Okay, I'm gonna write that as just to the one half because in a moment it will be convenient to combine exponents with other parts of the equation. Okay, well, let's see. We've got ideal vector all sorted out. R hat all sorted out. R squared all sorted out. Now we can plug this into the BIOS of our book. And I'm going to assume that you're at this point, if you weren't at the beginning of the course, you certainly are now that you're capable of popping up in a book and figuring out what an integral's supposed to be or flipping to the formula sheet on the exam and reading off the result of an integral or asking Wolfram-Alfra, how do I integrate this? And then getting the answer from it, okay? We're gonna kind of skip steps for the integrals and then a miracle's going to occur and we're just gonna move on with our lives, okay? So we need the little db vector due to this little current element I've written here. Well, the easy part of the constants out in front, you're not over four pi, they never change. Now let's deal with the numerator up here. So we've got idl vector. Well, that's idx i hat cross product. With r hat. Well, r hat's a little more complicated, so let's see here. So this is going to be, let's put the numerator of r hat up here. It's this thing, negative x i hat plus dj hat, okay? And then down in the denominator, we've got r squared in the denominator of r hat, which is x squared plus d squared for the one half. So I can already simplify this by multiplying these two denominators together, okay? So let me rewrite this, mu naught over four pi. In fact, let me just group mu naught and i together up here. Mu naught over, mu naught i over four pi. Put the dx here on its own.  And in fact, the integrals that we have to do here are eerily similar to the integrals that one has to do for the electric field due to a line of static charge, or any line of charge, okay? So if you dig way back in your notes, you'll see that we had to integrate something just like this. All right, so let me go ahead and now, let's see, I think I've got all the pieces. So let's look at just, let me just look at, so look at the cross product by itself. I'm gonna just isolate that little piece up here, okay? So we have i hat cross negative x i hat plus, I'm just distributing the cross product, i hat cross dj hat.  There's a gift, i hat cross i hat is zero.  Okay, well we have this one left now to deal with. So that thing's zero, so we have zero plus whatever this thing is. So I can pull the d out in front, that's just a number that multiplies either the i hat or the j hat. Again, a cross product is just like a multiplication sign and the same algebra like rules that apply to algebra distribution and so forth association. That's all that holds here. This is d is just a number. It's not a vector, it has no direction.  Now what's i hat cross j hat? K hat. d k hat. Okay, well let me go ahead and rewrite this thing now. db vector using what I've just learned. So I've got mu not i over four pi, I got dx. And now I have just the distance d k hat up in the numerator. dx squared plus d squared for the three halves. And that's about as far as I can take this thing without integrating it. So let's take a look at this. This has got all the thing, well it's got the key thing that we kind of anticipated at the beginning. So right now we've got mu not positive number, i positive number, four pi positive number, dx we're gonna integrate that away in a second. We got x squared and d squared. Even if those are negative, they become positive by squaring. So this whole thing in the denominator is positive number. And d by construction is a positive number. So we have a positive number times k hat. Number times k hat, we've done a good job. We can use the right hand rule to anticipate what the answer should look like. We can check to make sure the answer looks like that when we get through all the math. That's the nice thing about the right hand rule. It gives you a chance to think about things slowly, write a few notes down, and then proceed blindly into a blazing calculation of mathematical stupendous tricks or whatever this is, and then hopefully check your answer at the end, which is more valuable than anything else. Okay, awesome. So now we have to do an integral. So let's do an integral. Is it okay if I clear this out? Yeah, not a whole lot going on here anymore. Okay, so now to get the total magnetic field due to every current element in that liar, I have to do some integral over the little db vectors. Okay, so that's gonna be an integral over mu naught i over four pi dxd over x squared plus d squared to the three halves. Ah, k hat. Well, I only need to integrate over things that have a dependence on x. And so I can take mu naught and put it out in front. Could take i, put it out in front, no dependence on x, four pi out in front. That d, that d can go out in front because it doesn't depend on x. Now this nasty thing in the denominator depends on x, so I gotta leave it in the integral. And k hat doesn't depend on x, so I can move it out. So this winds up being an integral of mu naught i over four pi d k hat integral of dx all over x squared plus d squared to the three halves. And remember I have my limits of integration from before. I'm going from x equals negative infinity to x equals positive infinity, infinitely long wire. Now that's an integral you can look up in a book, ask school for an alpha for the answer, whatever you feel like you need to do. Okay, so I'll just write down the answer. It turns out that the answer to this is just two over d squared, that's it. Not a bad integral to have to write down the answer to at the end. And so we can just plug that in for that integral and we're done. We've got the magnetic field around a wire at a distance d from the wire is just mu naught i all over, we've got a two in the numerator and a four in the denominator, so we're left with a two in the denominator, pi and d is not quite it, okay not. Okay, that is the direction and magnitude of the magnetic field around a long straight wire, which essentially is what B.O. and Savart used to understand the law they wrote down later in the beginning. Let's look at the elements of this. If I double my distance away from the wire, if I go from d to 2d, I cut the strength of the magnetic field in half. So it has a linear dependence on the distance you are from the wire. So it goes as one over the distance from the wire. Similarly, if you remember for the electric field from a line of charge, that also fell off linearly with distance. So if we were to draw what these magnetic fields and electric fields look like from a current. So let's say I have a current coming out of the board. Okay, so it's coming at you out of the board. Let's just think about the electric field lines from the charges that make up this current. They are going to radiate outward from the wire. So the electric field lines, okay, so there are the ease and then through the number of technology, the magnetic field lines on there at the hand, they go in circles around the wire. We saw this from an experiment. Let's go back here, here. So that's what the magnetic field lines look like. And let's, too far, there we go. Let's, so again, let's kind of look back at this wire picture for a second here. If I'm up here at this distance d, viewing the magnetic field and I use the right hand rule to figure out what direction the magnetic field points. Remember you do current, that index finger, middle finger points along our vector, thumb indicates the direction of the magnetic field. If I go out here and I observe the magnetic field from, again, a distance d, but now along the positive z-axis, okay? So now what I have to do to get out to that point is I have to point my finger along i. I have to point my middle finger out toward that point p and my thumb indicates the direction of the magnetic field. So up here, the magnetic field points out. Over here it points down. If you go below the wire, it points into the board. If you go behind the wire, it points up. It's circulating. And so the magnetic field around a current carrying wire looks like this. This is a rich set of phenomena. Every time you elect chord on the floor, that thing in principle is emitting electric field lines radially outward. So charges could be accelerated by it along the radii. And it's got a circulating magnetic field around it, okay? Such that if a charge was up here and started moving toward the wire, its velocity would be at right angles to the magnetic field and it would start to bend in the magnetic field. All right, so apart from the various reasons you wanna shield a lamp cord from being touched. You don't wanna electrocute yourself. Shielding, like putting plastic around this, is also useful for basically dimming the electric field lines that come from a wire and the magnetic field lines that come from a wire. So that there aren't stray electric and magnetic fields all over the room, yeah. Can you do the right hand rule for the two points inside? The two points? Yeah. Okay, so what I wanna do is let me actually, or it doesn't matter where I do this as long as I get my directions right. So if I put my hand up at this point P and I point my index finger in the direction of I, which is along the positive X axis. How does that always point your index finger in the direction? Well, you always point your index finger in the direction of the first vector and then you point your middle finger in the direction of the second vector, so A cross B equals C, always, yeah. So A, B, C, or in this case, D, L, R hat, B. Okay, so up here, that's where the magnetic field points. Out here, you have to rotate your hand and this is really painful, I promise you. You still have your index finger pointing in the positive X direction, but now to get from the current element out to this point, you have to follow a line indicated by my middle finger and so your thumb points down and that's about as far as I can, as long as I can. All right, so let me construct this and then. All right, so we're gonna do like, this is where having one of these all pre-built would be really handy. So, all right, so there's my little coordinate system, okay? So, D L vector point this in the direction of R hat, that indicates the direction of the magnetic field. So if I apply that here, okay, I just have to adjust that back so that it points along R and then the magnetic field is at right angles to both of them, okay? So I can translate that up here, that's what that vector would look like. And if I go out here, I have to rotate this so the green still indicates the direction of the current. The R vector points out this way, okay? And magnetic field now points down, okay? And then if I rotate that around one more time, I keep going and this is a circulating magnetic field line. Okay? There's actually an easy way to remember. There's another right-hand rule, you can bust out. There's always another right-hand rule. You can remember which way the magnetic field lines are circulating around a segment of a wire.  So, thumb out, current, and look at that, they curl in the direction of B. If the current pointed in, the magnetic field lines would circulate in the opposite direction. So this is another way you can remember. Current, sense of rotation of the magnetic field. All right, so I already went through that. All right, so we went through this. So the, well, okay, so this is just the wire again. I already went through the right-hand rule. Okay, so something I wanna talk about now. What are the consequences of the B.O. Savart law? Let's go back to the wire again. All right, so the magnetic field from a wire, if, let's focus on wire A up here. So I have a long wire labeled A. It's carrying a current that way, so I'll point my thumb in it. And if I curl my fingers around my thumb, that tells me the direction that magnetic fields are circulating around this wire due to the moving charge. So the magnetic field lines are circulating out of the, this is sort of a funny angle, around at right angles to the wire. What are those magnetic field lines doing? There is another wire over here, and it too is carrying your current, I, B, let's say. So wire B points in that direction and suddenly it encounters a magnetic field due to the first wire. What happens when you have a current traveling through an external magnetic field? What does the current do? I failed as a teacher. I failed. That's it, they won't pay me this year. External magnetic field, B, caused by something else we don't care what. I, traveling through the magnetic field along some line L, hint hint. What's that? Yeah, there's a force due to that external magnetic field on the other current. So if the source of the magnetic field is another wire, which we know from B.O. Savart, is absolutely possible, in fact very likely, this wire will feel a force due to the magnetic field from wire A penetrating the current on wire B. All right, so where does that magnetic field point? Well, it's circulating around wire A. So over here it points down, and that's what's indicated here. B vector magnetic field due to wire A points down. And so if we think about the forces involved, we have a current, a magnetic field, I L cross B, and then the resulting, well, I'm trying to do this way, the resulting force points toward the other wire. This wire exerts a force due to its magnetic field on this wire that pulls them together. And if you look at the problem the other way around, well, what about B? Doesn't B cause a force on A? I mean, B carries a current. It's got a magnetic field that circulates around it. That magnetic field penetrates the conductor A, which is carrying a current I A. It too feels a force, and that force points from A to B. So they pull each other together. When you have currents pointing in the same direction by two neighboring wires, they exert mutual forces on each other that cause the wires to move together. If the currents point in opposite directions, they repel. So this is a bit like two, a north and a south pole next to each other, a north and a north pole next to each other. Has anyone ever been under high voltage power lines before? Anyone ever gone running or hiking in the wilderness around the city, just walked, like maybe by the Cady trail or on the Cady trail. I think there's some high voltage lines that go over that. Has anyone ever done that before? Morgan? Yeah? Or is that just the pen in the air? Okay. Lynn? Yeah? What have you noticed? What have your senses picked up when you're around high voltage power wires? It's something really obvious. Yeah, loud crackling sound. Actually it's a buzzing sound. It sounds some, well, okay. So that's what a high voltage, a high tension wire looks like. All of these conductors are stuffed together in a single bundle and they're all carrying current in the same direction. And actually they carry alternating current. So we're not gonna cover this in the course but alternating current is sort of just what it sounds like. For one moment in time the current points one way and then another moment in time the current goes to zero and then it points the other way. And then it goes back to zero and points the first way. This was, this way you get a very good transmission of electricity at low loss over long distances which is important in an electric power transmission system like in the US or any country, okay? So alternating current is just the current goes one way in let's say one sixtieth of a second and it goes the other way, the next sixtieth of the second and then back and forth and back and forth and back and forth and you can still do work with that current and after all that's what we want. Alternating current is what powers the lights in here, alternating current is what comes out of this wall socket here and you can analyze it, it's a whole chapter in the book on it, we're not doing it, okay? But it is consequences. And that means that for one sixtieth of a second all the currents in these wires point one way. So what do the wires do? When they're at max current going one way what do they do? They're trapped. Then the current goes to zero. What happens to the wires? They pull apart. Now the current flips the other way. Again all going in the same direction. What do the wires do? Attract. Then they relax, then they attract, they relax and they attract and they do that about 120 times a second, okay? So if I could do that 120 times a second this is what you'd hear. So coming out of this little section of trail come out to this power line, it's making like a buzzing noise. Hope you can hear it. It's not the happiest noise I've ever heard a power line make. All right so the power lines make a little buzzing sound. Like that. That buzzing sound is from the mechanical force of the wires actually colliding with one another in the bundle. Okay so this is why it's important to when you design systems like this or if you're working with systems like this you need to be aware that any high current carrying wire with other wires near it will cause a deflection of the neighboring wires toward the high current carrying one because of its strong magnetic field, okay? Let me bring these slides back up. All right so there's one more thing I wanna show you and this is something I hinted at before but now you can really see it, okay? And that is an MRI machine and what happens if there are strong magnetic fields and high current carrying wires. So I'll show you this image first, okay? Give it a second. So this is, I'll go into this thing next lecture, all right? This thing is called a solenoid and it is nothing more than a bunch of loops of wire placed right next to one another. I'll show you one in class next time. They all carry current I and together they make a big magnetic field in the center of the loops. It's very uniform. In fact it's almost perfectly uniform if you design your solenoid correctly, okay? Got two minutes left here folks. And this is great for human beings. Once we learned that there's something called nuclear magnetic resonance, that is that you can expose nuclei to alternating magnetic fields and get them to sympathetically flip back and forth in the magnetic field and by doing that, looking at the frequency you can figure out, oh that's calcium, that's fluorine, that's carbon, all right? So you can actually identify atoms in a substance, in a material. You can then put a human being inside of a very long, straight, powerful magnetic field, get all of the little electronic and nuclear, most importantly the nuclear spins in their body to all point in the same direction because they're all little dipole bar magnets, okay? And then you can blast the body with radio frequency waves which causes the bar magnets to flip in the magnetic field and the frequency of the flip can be used to image the body. So that's what a computer aided imaging of the magnetic field of one of these MRIs look like. Note the scale, the red is one Tesla. These are really big magnetic fields. They go up to two Tesla. In contrast, the magnetic fields in my experiment, the Large Hadron Collider, which we use to steer protons, they go up to like six, seven, eight Tesla. They're really powerful magnets. When they explode, it's catastrophic, okay? And that happened in 2008, all right? So here's why you should secure your high current carrying cables going into your MRI magnet because there's leaking fields outside of this really powerful solenoid, okay? This really powerful big loop of current. So there's the MRI magnet and this is a trailer.  And so it looks like, let me go back and do that again. All right, it looks like they're flapping in a breeze but they're actually whipping back and forth. I mean, those are really thick cables whipping back and forth almost effortlessly in the stray magnetic fields of the solenoid, all right? Okay, we'll pick this up next time. Thank you.


finance, energy and war. So Biden today banned the importation of oil and gas from Russia. So Americans cannot buy oil and gas from Russia. Again, I'm skeptical about all these things.  Why are you selective? Why don't we just embargo Russia? No goods in, no goods out. You can export, you can import and just shut down trade with Russia. I think that is the right approach. If you're going to use trade in this way against what you perceive now as an enemy, then you will boggle the enemy. It's okay to trade for Russian dolls, but it's not okay to trade for oil. No, it's not okay to supply money to the enemy. And trade is supplying money to the enemy, and therefore you shouldn't do it. So really, what we should do is have a complete embargo on it. Mr. Book got a message of hope and optimism from Ukrainian friend watching the show now. Also, the show, keep up the good work, man. Yeah, I mean, I've said this on the previous shows. I'll say it again. If there's somebody from Ukraine listening, I'll definitely say this. Look, Ukrainians are being amazing in this conflict. They are odd guns. They are odd manned. They are not a people really prepared or have experienced with war. They were invaded in 2014, but that went very quickly. There wasn't much of a war there. And Ukraine have done phenomenally well. I don't know if they trained well or prepared well for this. I don't know if it's just a spirit, but they have rallied to the cause. And the president has been truly amazing. I've said this before, I think, to the most impressive politician on the planet right now. I can't think of anybody else, even in competition. He is truly amazing. He's rallied his people. He's put pressure on Western governments to help them out. Mostly, he's been effective in doing that. And Ukrainians are holding them back, right? Ruk Solana says she's in Ukraine but currently in Georgia. I'm hoping to be in Georgia at the end of April, early May. So I've got scheduled talks on April 30th and May 2nd in Georgia, in Tbilisi. So maybe I'll meet you there. That'd be great. And I think the Ukrainian people have really showed up and good for them. Again, they've got less equipment but better equipment. They're using Western equipment rather than Russian equipment, although they're still flying Russian planes and doing quite well there. So overall, I think this is a good step. I think if the Ukrainians, the Ukrainians that are fighting should be proud of what they're doing. They're holding this Russian bear. They're fighting for their own freedom. Hopefully if they can win this or hopefully one day when the Russians leave, Ukraine can become more, even more of a free country. I mean, the real upside for Ukraine is to use this as an opportunity to really rethink what it means to be a free country and reinvigorate whatever freedom, liberty movement they have. And whatever the fate coming out of this, they will come out of this, whether it's this year, next year, five years, 10 years, 20 years to come out of it stronger and more committed to freedom and liberty than ever before. So hopefully that's part of the lesson they learned and it can become. I mean, as I've told you before, Atlas Shrug was the best-selling book in Ukraine in 20, I think it's 2014-15 or around 2015. I think there are some amazing people there and who knows what the upside is if they're truly free. Look, Solana says Georgia has a pro-Russian government. I know it's super sad, particularly considering where Georgia was 20 years ago, how free it was, how pro-capitalist it was. It was maybe the most pro-capitalist government in the world and that is all gone and lost. And I'll be in Georgia to try to inspire more activism towards capitalism. All right, James asks, what is the long-term impact of private companies punishing Russian citizens because of the war? Do you think it will create resentment of the West? Also, how does this help China long-term? China buys 20% of oil from Russia. Okay, a few things. I was going to talk about this in terms of energy, but in terms of the companies, I mean, I think it's a short-term hit to the bottom line. Russia was a market. As I said, Pepsi, it was a third of the market, third largest market they had. It's certainly going to take a short-term hit. But I think that long-term, these kind of things could prevent China from taking Taiwan because China doesn't want this. They don't want private Western companies to cut them off because China would be devastated if that happened. China has much better understanding of the benefits of trade than do the Russians. And China is looking at this and saying, God, the West is really serious about these sanctions, about limiting trade, about these companies leaving. We don't want Apple to leave China because we invaded Taiwan or something like that. And you've got to imagine that Apple today is working through contingency plans of what if they had to leave China? What would happen? I really do think of all the activities these private companies are doing might be the thing that ultimately motivates the Chinese maybe a little bit to behave more than anything else the US government could do because they don't want to lose touch with these American companies, which are the real source of benefit they get from the West. So the companies will take a short-term hit to the bottom line, long-term who knows because who knows what will happen in Russia. Yes, this will definitely build resentment to the West on the part of the Russians and maybe in the part of some Chinese. But I think China has no options. It's not like they have other brands that can easily replace the Americans, although in some cases they have replaced them, but in others it will be different. And so they'll take up a financial hit short-term. I think long-term it might be hopeful because other regimes will think twice about doing this kind of stuff and that'll prevent them from getting in these situations. And I think these companies benefit in the goodwill they generate in the Western Europe and in the United States and much of the rest of the world. So I definitely think they gain goodwill and maybe some revenue as a result. I'm much more likely to go and interact with the company that is with a company that just took up a stand than with other companies. So let's talk about oil. Let's talk about oil. So as you know, Biden just make it illegal to import oil. Oil prices are going up because people are worried about shortages or becoming the supply of oil and therefore prices are going up when you restrict supply or when people expect supply to be restricted prices go up. I don't know that this action by Biden will actually affect the supply of oil because think about it this way. Since Russia doesn't sell its oil to the U.S. so what does it do? Oil markets are international markets so that oil will be sold somewhere else. India, for example, has already said that it is willing to buy Russian oil. Now it's going to be more complicated to get it to India than it is to get it to the United States. India won't, for example, finance the shipping. They won't accept delivery at the ports in Russia. They'll only accept delivery at the ports in India. China might take more Russian oil although again Russian oil is heavy oil. You need particular refineries to deal with it. It's not clear that China can take more Russian oil than it already takes. India, I think, has a refining capacity to take more Russian oil. I've seen countries like Malaysia say that they intend to continue trading with Russia. Potentially they would buy the oil. So because oil markets are international, if the United States stops buying that doesn't really affect the flow of oil. We get oil from somewhere else. Now where do we get the heavy oil that Russia provided that Canada could provide but we don't have the Keystone pipeline Venezuela used to provide but we're not trading with Venezuela? Well, it turns out that we might be talking to Venezuela. Todd says the U.S. Open Dialogue with Venezuela, how distasteful do you find that? Very distasteful. I think it's horrible. I don't know if Mexico has the same kind of heavy oil as comes from maybe. I just don't know. Todd, thank you. Wow. That is fantastic. Todd says my firm unnamed has departed from Russia. I am proud of that decision. See, it motivates employees too. So Todd just put $200 behind that. So thank you, Todd. That's very, very generous and that gets us very close to $600 today, which is terrific. What were we talking about? Yes, so Venezuela. I think it's horrible that we're doing that. Venezuela is an evil regime destructive to its own people. I don't think we should be trading with Venezuela. In our hemisphere, we have every interest to replace that regime, but it looks like oil rules and we will be talking to them. James says, what is the impact of getting off of Venezuela? They are an ally of Russia. Yes, they are. What stops us from getting off of Canada or using more oil in the United States? Canada oil, it's a matter of transportation. We don't have the Keystone pipeline, so we don't have a pipeline going down south from Canada. We can use trail train cars, but that's a much more expensive, cumbersome, messy way to transport oil. We're probably doing that as we speak. We'll probably import as much oil as we can from Canada through train cars, I think is the main mechanism. We could go for more oil in the United States. The oil in the United States is a different kind of oil. It's a lighter oil. I just wanted to point this out. Before you get to US oil, which I want to focus on, so the oil market is an international market. The Russian oil is going to sell in world markets, but what's interesting is that if you look at Russian crude right now, as compared to American crude or Saudi crude or anybody else's crude, it is selling at a significant discount. The reason it's selling at a discount is that Russia right now is trying to sell the oil. They'll sell it to anybody who's willing to. Putin is not benefiting as much from the increase in oil prices as one would expect because he has to sell it at a discount for anybody to buy it, because the Indians are not going to buy it at market prices like anybody else's. They'll only buy it because there's some political risk and some other risks. They'll only buy it at discounts and they'll only buy it, as I said, once it arrives at a port in India. It's not easy for Russia to deal with this, but it's not like suddenly they can't sell all this oil and their revenue goes to zero. No, they just sell it to other parties and maybe they get a lower price for it, but they're still going to sell oil. Again, this is the same problem with embargo on oil from Iran. All markets are global markets. As long as somebody will buy their oil, they will sell that oil and India will buy less American oil and buy more Russian oil or less Australian oil and more Russian oil, whatever, but the oil will be sold. Everything that's pumped up, demand will be met. In other words, all the demand that's out there will be met. It's not as Biden said, oh, we're hitting them where it really hurts, not really. We're making life a little bit more miserable for them, but this is not some dramatic thing. Revenue for more right now is skyrocketing for Saudi Arabia for US producers and skyrocketing, so they're making huge profits right now, huge profits. This will be an amazing year for them because they're pumping out oil, they're selling it at the highest prices we've seen in 14 years. Travis said Saudi Arabian oil revenue up 150% over a few years ago, absolutely, because prices are up more than 150%. Now, why don't US producers start producing more? Well, first, because it's not clear the demand is there. So producing more would lower prices, but it's not clear how much more demand the world economy has, particularly if things slow down in the world economy. But second, drilling all requires a lot of money. It requires financing. It's risky. Not every, in spite of how sophisticated our technology is, not every oil rig pays off. American oil companies have a lot of licenses now from the government, but they need funding to drill. And they need to be convinced that if they drill and start producing that production won't be taxed or won't be shut down in a year or two. If they're going to make an investment today, they need some confidence about the future. And they don't have that confidence. And this is where Biden and the Biden administration is particularly bad. This is one area where the Trump administration was good, not necessarily Trump, but the Trump administration was good. They basically were very pro oil and gas and coal, and they allowed them and they gave them confidence that at least while that administration was in power, they would have, they would be able to profit off of the oil rigs that they drilled. The Biden administration is doing the opposite. Its regulatory agencies are currently writing new regulations to regulate the oil business. The Federal Reserve is being asked to start regulating financial institutions and the other bank regulators, all the different regulators of financial institutions and then many of them, six, seven different ones. They're all now being asked to consider climate change and how they regulate banks, which is a whole show I will do at some point because it's a dumbest idea in history. And part of this will entail banks not being allowed or limited in how much they can lend money or they can finance oil drilling. So people, I met a guy who's raising capital in order to finance oil drilling to replace the banks, but that is, it's going to take time. It's more expensive capital. And again, because of ESG, environment, society, environment, no, wait a second, ESG, environment, society governance. This is the leftist way of taking over corporate America. All companies are just not motivated and are not incentivized to drill. They don't know what's going to happen next year. They don't know what these new regulations are going to say.  We'll drill. You have to freeze all new regulations. You have to not promise not to penalize us later for the drilling we're doing right now. And it's real suicide, economic suicide, what the Biden administration is doing. But of course, we knew this.  If you listen to some of the nominees of the Federal Reserve talking about the systemic risk of climate change and how they're going to try to get the Fed and financial regulators to reduce climate change risk, the systemic risk involved in finance, it's complete nonsense. And these people don't know what they're talking about and it's an authoritarian takeover of both banks and of, you know, and it's a takeover of our banks as if they're not taking over already, they're already taking over. But and it's a complete anti oil and gas agenda. And oil and gas companies are saying legitimately, well, we're not interested. What's interesting is, is we're seeing that a lot of the environmentalist movement, a lot of the anti oil and gas movement, a lot of the climate change movement in Western Europe and in the United States has been funded by the Russians. It's amazing how much money the Russians are poured into environmentalist groups to try to prevent them from fracking in the UK, fracking in Germany, fracking in Ukraine, fracking in Western Europe where there's a lot of natural gas. And of course, in the United States, the Russians have been funding environmental, the environmentalists heavily in order to discourage the local developer of energy. So they could be the primary, they want Western Europe to be completely dependent dependent on this. So this is again ties into the whole Russian propaganda thing. They're very good at this. Thank you. I very much appreciate it.


back to my channel. So today we've got another meal prep video. If you're new here, I do these about every two weeks, so twice a month. So that's why I call them monthly freezer prep videos. My freezer is not that big. We eventually want to get a deep freezer for in our garage, but for now, if every two weeks works out the best for me, I can kind of stock up and then replenish as things run out or just be making new recipes. So the whole idea behind this is I try to make healthy things that we can use instead of just buying a bag of chicken nuggets, you know, things that work quick and easy. And I've been getting questions about how I reheat these meals and the things that I make for in my freezer. And it's kind of a combination. I do use the microwave at times. And then we recently got an air fryer, which that's been awesome. I've been using that a lot to reheat things. So yeah, I will leave the playlist below of all of my meal prep videos that are similar to this because I know that you guys really enjoy those style videos. And I have a lot of great things to make today. First thing that we're going to dive into making is some chili. And to be honest, I've kind of gotten into a thing of having chili in the freezer most of the time. And my husband knows it. And the other day he went to make some chili dogs and he's like, there's no chili in the freezer. Just because it's such a simple meal if we need it really quick. And obviously making chili dogs is also a perk whenever you're in the mood for that. So what I like to do is make a pretty big batch and then divide it out into like two portions. We may actually have one of the portions for dinner tonight just because since I'm already making it, we may just eat that. I make my chili without beans. I just started doing it this way a few years ago and really prefer it. And I don't have exact measurements every time I'll show you everything that I'm going to be putting in it today. And you can kind of get the gist of like what I use as a base to make chili without beans. Also wanted to address something really quick. I've been getting a ton of comments about plastic wastes and you know using freezer bags or saran wrap and things like that or just like reusable containers stuff like that. And sometimes I do that out of convenience, but I've been hearing you hearing you and I've been doing a little bit of researching and so I have some reusable silicone gallon bags coming. They're not here yet. So today I'll be using disposable, but I have some coming to try them out to see if I like them. And then I will let you guys know some options that might work well for reasonable things that you don't have to be constantly using plastic and throwing it away. That sort of thing. Sometimes it's handy just to not have the extra dishes to do on a really busy day because most of the time when I get things out of the freezer it is on a busy day and it's just easier for me to be able to like throw away whatever um everything is in. And of course if you're buying a bag of nuggets at the store they're in a plastic bag. If you're buying dinner at you know takeout they are in something that's generally recyclable which plastic bags are. So just keeping those things in mind. Moderation in life everywhere you are I always talk about moderation and there are sometimes that things like that just save us moms a little bit of time and one less thing to wash. My favorite way to make my chili is in my Dutch oven. So this is if you've never seen something like this it's basically like a stone it would be similar to a cast iron skillet but it is a big pot and it has a really heavy lid. The whole thing is pretty heavy. I've had this one for a pretty long time and I'm actually I have about a pound and a half of meat in here. I just took a three pound block and like split it in half but you could put two pounds in easily. It's just ground beef and then I put the lid on. Basically what this does is it's similar to a slow cooker. So you really could use this like a slow cooker you could put a roast in it put it on low on the stove and just let it really cook low. So that's why I like to make my chili in here because it kind of gives it the taste that it's been sitting cooking a long time when it really hasn't something about the way that it keeps the heat inside does a great job of that. So I've got this on I just threw it in there didn't put anything else in there and I'll show you what I'm going to work on while this is getting cooked up. So one of the things I really like to put in my chili as a base since I'm not using beans is rice cauliflower. So that is what's in this bag. So I'm going to be putting this in and then I also love to use bell peppers. I just think they're so sweet and delicious in chili. So I've got three bell peppers. I don't know if I'll use all of them. I'll kind of cut them up and put them in one at a time see how it goes. I need to wash them and then I also have an onion and sometimes I've even done a bigger onion than this. Like I said it's not exact measurements but you're getting the idea and then I have some diced tomatoes and then some tomato sauce. So I'm going to get all of this I'm going to get these diced up and the onion diced up until then the meat should be probably kind of close to being done. And then I put this stuff in with the meat once it's like almost browned and start cooking the veggies and as they soften then I add in like the sauce and the tomatoes and the spices we'll get there. Once you see the onions start to get a little bit clear means that they're getting cooked through. You're going to let this simmer when you're all done mixing everything together but I just like to make sure that stuff is like mostly cooked till I put the tomato product in. So I'm going to be putting the tomato stuff I showed you a little bit ago and then also some chili powder, some onion powder, some cumin and garlic and to be quite honest with you I shake it in as I go. I just kind of know and taste as I go and figure it out from there. Also some salt and then if I want it to be a little bit of a sweeter chili I'll add in some stevia. I'm probably just going to let it be today instead of doing the sweeter chili and then the other thing I throw in is the rice cauliflower but you don't really want to do that until you add the tomato products just because it already is kind of like it cooks up really fast. You wouldn't really want to add that into what's going on now. Just came home but I wanted to let you guys know that today's video is sponsored by Skillshare. I've worked with them quite a few times before so if you've been around my channel long enough you know how much I really love them and they've been my favorite sponsorship I've ever done just because I'm so about learning new things and picking up on new skills and I'm also a very visual learner and Skillshare really brings that to the table whenever you're trying to learn something new. Skillshare is an online learning community that provides thousands of classes. The range is honestly amazing. They've got anything from culinary classes so if you want to learn how to do some different kind of cooking or photography, design, even classes on being more productive which I can always use in my life. Skillshare is for anybody. It can be from somebody that's a master in something to just a beginner. Obviously right now we're all doing a lot of social distancing and being at home so this is one way to fill your time with doing something super productive. It's also a good way to calm your anxiety or just get your mind off of maybe some of the stresses of life right now. The Skillshare community is also a great way to meet other people that do things that you enjoy as well and make new connections. So if you guys are interested in trying out Skillshare which I highly recommend, I use it myself. The first thousand people to hit the link in the description box will get two months free to try out Skillshare and you guys will definitely want to keep using it. It's something that I've been using for quite a few months now. So back to cooking, back to what we've been working on. So the chili, one of the thing I wanted to make a comment about is we like our chili a little bit thicker and you can add water to it and thin it down but one thing that that frozen rice cauliflower brings to it is it does bring some liquid in. So I didn't add any water or broth or anything like that just because we like it on the thicker side and the added liquid it needs was already there. You guys have been watching for a while. One thing I really like making for my girls as a healthy snack is ice pops. So I get these baggies. I have to grab them actually and I'll show you in a second off of Amazon. Always leave them linked below but they're a really great way to fill your own ice pops with healthy ingredients. So today we're going to make some with some pineapple and some strawberries. I'm just going to throw it all in the blender and add probably a little bit of water or almond milk just to water it down and then fill up the ice pops. Add any water to this. It had enough liquid in it and my girls always love these. We've been out of them for a while so they're going to be so excited when they wake up from their naps and see that I've made a bunch of them. So these are the bags. I hope you can see them they're a little hard to see on camera but they're the kind of like a long skinny ziplock bag and then I take a funnel and this does come with a funnel. I use a little bit of a different one that I have but it does come with a funnel and then you just fill it up and I have put yogurt in these. If you guys go back through my meal prep videos you will see that I've put a lot of different things in these and they're just a really great way to get a lot of nutrients into your kids and they don't really think about it because they already love ice pops and it's something that they want to eat. So I'm going to fill these up in between doing some of my other cooking. Actually the next afternoon I decided to film this over two afternoons just while my girls were taking naps. It's a little bit easier for me to get stuff done obviously whenever they're sleeping. So I'm going to be doing some french toast in the air fryer. So I got some gluten-free bread from Aldi here and I have eggs, milk, heavy cream, cinnamon, sugar and then some vanilla. I'm going to link the recipe I'm using below but I think I'm going to go about it a little different way. I'm going to mix the eggs, vanilla, milk and heavy cream together and then flip the bread in that and then I think I'm going to make a mixture with the cinnamon sugar to put on top right before I put it in the air fryer. So I'm going to test it out and you guys can see the result. I think it's going to turn out well. Obviously the more traditional french toast would be with like Texas toast style bread, the thicker bread but since we have some gluten sensitivity and I try to do things that are gluten free we are going to try out this bread. I've never done this before so we'll see how it goes. While I'm working on putting the french toast sticks in and by the way I'm trying out individual sticks I think it'll work out good that way. I may end up just putting whole slices in but I actually think I can get more in the air fryer when they're cut before they're fried. So going to see how that works out. Now I'm going to make something that I've actually made before and this is a really great alternative to the packets of oatmeal that a lot of us use that you can heat up really quickly. So I have these muffin silicone liners. They are from Amazon and what I do, there's a recipe for this. I will link below but this is my own version of it I guess if you want to say it that way. You have to use Quick Oats just because the rolled oats dry out a little easier and this reheats a little bit better than the whole oats. So we're using some Quick Oats and then what you do is you cook it up. I have some milk here and then she suggests using brown sugar in the recipe but I like to use this pure uh stevia sweetener just so that they're not getting all the sugar which is kind of the point of doing this instead of the packets just because there's a lot of sugar in the little oatmeal packets and then so you cook that up and then you put them into these and you top it with fruit. The girls like some shredded coconut that kind of thing and then I put them in the freezer let them freeze the whole way through and then you can just pop them out and keep them in a container and all you got to do is grab out the cup throw it into a little bowl and warm it up in the microwave or you know whatever you want to heat or stuff in and it's a really fast way to have oatmeal. The last time I made these the girls really raved about them and I think it's definitely one of their favorite breakfasts. It's taken a little bit of experimenting to figure this out so I started doing them in three like one piece since they're a larger piece of bread. I did them in three strips and this was my first batch they were a little bit too dark so this is my second batch and now this is my third batch and I'd say that they're looking really good really great to reheat you don't want to overdo them because you will heat them again whenever you get them out of the freezer but I think it's going well and what I'm doing is the first side I'm doing four minutes at 375 and then I flip them over and I do them three minutes and then they're done. The next thing that we're going to make is some chicken patties I've actually been wanting to try this out for a while just because I feel like it's a super rounded meal idea lunch idea for kids so I've got two chicken breasts in here I just cut them in half I put about a cup of water in so I'm going to put those in my pressure cooker cook them up you could cook them any way you want you can put them in your oven, fry them on the stove whatever but you do want the chicken to be able to kind of shred so I find that doing it in my pressure cooker makes them soft and I can kind of shred them up and they'll go into the patties really easily and then I'm going to be putting some of these just quick mixed vegetables into this pot and cooking them up these are going to be my veggies that are going to go into the patties. So this is a cup of these veggies it's two chicken breasts and then I'm going to be putting in a cup of this gluten-free flour you could use regular flour you could use a keto flour mix whatever you want I've never tried this before but it's kind of convenient they come in individual packages of one cup so you can keep them for a long time and they'll stay fresh and I'm going to put in about four eggs and then I'm going to put some dill weed some salt and some onion powder we're going to try out that consistency like I said this is my own recipe I'm kind of coming up with it as I go so I'm going to mix it all up and then see how it seems if it's a little bit runny I might have to add in a little bit more flour but we'll see how they go all right so this ended up being a really great consistency I'm super happy with it so I'm going to put some olive oil in the pan and then I think I'm going to try using a cookie scoop to scoop them in and then kind of flatten them out so they're going to be really small I would say like pretty bite-sized but I want them to be finger food size so that the girls can easily eat them so we're going to try this out and if for some reason they're not cooking through or something like that I may add another egg I actually think that they're a little bit thicker the batter or whatever you want to call this is a little thicker than I expected it to be but I think it's going to work out these turned out so delicious the girls really enjoyed them and I enjoyed them myself I definitely think I can do different variations of them and they're so healthy and just a great lunch option I hope that this video inspired you guys don't forget to check out the links in the description box if you're new around here I'd love it if you subscribe to my channel give this video a like leave me a comment below I love reading your comments and getting back to you guys and I'll see you guys in my next video


Appalachian Wireless is Appalachian Advantage. Unlimited text talk and two gigs of data for as low as $45 a month. Or if you like, get five lines on eight gigs of data for just $145 a month. Sea store for details. Better service, bigger savings. That's today's Appalachian Wireless and East Kentucky Network Company. Hundreds lined Weizberg City streets today to honor an American hero. Jenkins native Staff Sergeant Abigail Milam as a procession carrying Milam's remains made its way through several Eastern Kentucky counties to bring her home. Some residents in attendance felt it was their duty to be there to honor Sergeant Milam. The VFW especially understands what being killed in the service to your country and we we know that she was doing her part for our country and that and those that that support America should not be ignored. Eastern Kentuckians were always first in the battle and we always gave more than anybody and it's proven by the records of the government that we're always there when we're called upon to defend America. Others in attendance felt it was important for the younger generation to be there to experience the meaning of the price of freedom. I think it's really important for my children to be here because I think it's really hard for them to kind of grasp the concept of the sacrifices that people make for the freedoms that we have and I think this is a great way for them to actually see and feel and be in a moment where someone has given the ultimate sacrifice for for what we have and what we're able to do and the freedoms that we have in our great country. Services for Sergeant Abigail Milam will be held Saturday at 1 p.m. at the Hemp Hill Freewill Baptist Church in Jackhorn. Reporting from Whiteburg, I'm Sean Allen for EKB News.


I feel proud. I am so proud of what I'm seeing right now. I can't wait to see our solution go. I know she's going to do her best and we are sure that the best will be down to the benefit of herself, the country and the entire region. I'm very excited about it. 9. This exercise, ladies and gentlemen, will fall squarely within the intentions of this government. That is the beautification of our city. First of all, I would like to thank the CDF for setting this in motion. Although I've been painting murals for many years around the island, this one is by far one of the best projects I've done. So thank the CDF. Let's thank you to all the people of Castries. From the time we were preparing our manifesto, that we had to include in that manifesto the emphasis we would place on expressions like this. We made sure we included it in our manifesto because it means a lot to us. It means a lot to us to allow solutions to be able to express their solution-ness. It means a lot to us for our people to be able to say how they feel through arts. 8. The government of St. Lucia, led by Prime Minister, Honourable Philip J. Pierre, continues to fulfill its mandate of attracting foreign investment to the island. So I want to assure the Merlin family that the government will do whatever we have to do. All we ask from you is to be fair, to be fair to the people of St. Lucia, to be fair to the workers of St. Lucia, and to ensure that St. Lucia is at the top of illicit priorities. We are aligned with Minister O'Lear's initiatives and the promotion to promote guests exploring the experiences on the island and the economic impact it will have beyond the hotel. In addition to all-inclusive hospitality services, the property boasts more than 350 luxury suites and rooms. Secret Resorts is scheduled to officially open its doors in the summer of 2024. 7. The reunion primary school in Choselle will soon have a brand new music facility estimated at approximately EC $151,000 through the Caribbean Development Bank and the government of St. Lucia. A memorandum of understanding was recently signed between the reunion primary school's music committee and the SSDF to formalize funding for the music facility. Our children can demonstrate their greatness, they can demonstrate their humanity, they can demonstrate themselves in music in a way that it's an art that is so powerful. 6. St. Lucia's collateral registry of movable assets has reached another milestone in the implementation phase. The collateral registry is an online database of movable assets that support the security interest in movable properties act passed in parliament in 2022. This project entails two phases, the development of the software as well as the installation of the hardware and things are happening. The equipment is being delivered, the hardware is being installed today and we are very thankful. 5. Efforts at ensuring the injured hospital is adequately equipped to respond to the health needs of the people in the south of the island are underway. Following the recent handover of hospital beds, oxygen concentrators, pharmaceuticals, cardiac monitors, library agents and consumables to the hospital. Our government is very committed, Hon. Philip J.P. as Prime Minister is very committed to the health sector and we are very committed to doing the things that we must do now to ensure that the health sector remains strong. These supplies will allow the hospital to focus on delivering day-to-day care to patients and we are pleased that these items will augment equipment available at St. June Hospital and on the wards where they are needed most. 4. Staff of the Tirochet Casteries Wellness Centre and the Bureau of Health Education were later to engage with prospectants and nursing models in a breastfeeding education and sensitization session. Today the theme is enabling breastfeeding, making a difference for working mothers and we know sometimes the difficulty working mothers have in feeding their baby, expressing the milk, you know, getting time even at work to be able to express the milk so we are advocating that employers understand the importance of breastfeeding. 3. The Department of Fisheries and the Japan International Cooperation Agency have once again united for the ongoing Coast Fish Project which aims to strengthen the sustainable use and management of coastal fisheries resources in Karakam countries. What is often overlooked and underappreciated is the critical role that statistics and data analysis play in the effective management of these vulnerable resources. The issue of data, the management of fisheries and fisheries related resources, the analysis of data to inform decision making is very, very critical. 2. The World Health Organization declared that COVID-19 was no longer considered a public health emergency of international concern on May 5, 2023 due to the reduced incidence of cases in hospitalizations and deaths. Currently, the dominant variant of COVID-19 in St. Lucia is an Omicron Subvariant called XP1.5. As expected, over the period of increased mass crowd activities, during the last three weeks, we note an increased number of persons with respiratory illness, both in the public and private facilities. 1. The Ministry of Health, Wellness and Elderly Affairs, through its process of disease surveillance, closely monitors the dengue fever cases appearing in the country. To date, 14 confirmed cases of dengue fever have been recorded on Island.