Hi everybody, it's Barbara Tint with the Applied Improvisation Network and I am here to share a conversation with you with Ella Aman who is a long-standing friend and colleague based in Berlin Germany and I've invited Ella into a conversation with us because her work has been on resilience and applied improvisation and if there was ever a time when we needed to draw from our resilience, collectively it would be now. So Ella, thank you so much for taking the time to be with us today. Thank you for having me, Barbara. Nice to meet you these times, yeah. So you probably know some people who are watching this and many who you don't so maybe you can tell us a little bit about your work and how resilience has come into being during this time. Yeah, so I'm working in the field of resilience now since 25 years and collecting the work of resilience was applied improv also since 20 years, 25 years professionally and yeah in these days it's exactly what we need right now. We need the capacity of resilience so the natural capacity of the body, the mind, the psychological capacities of resilience and deal with crisis and deal with the unexpected and the moment of crisis is the moment when we can't move on with all the routines or habits or resources we have and when times of challenge, when the time is challenging us right now and we experienced the feeling of oh my god I'm so overloaded I'm stressed I'm not able to know what to do in the next moment then you have this little moment of a potential crisis and normally the body and the system and the mind are capable to be creative and open, start learning, improvising and then you find your way through this moment and it doesn't have to become a real crisis but when the circumstances and maybe your physical or also psychological health is not really stable then a crisis like now can be out of the balance and then you go into this mode of crisis so like maybe you're familiar with this the path of the crisis like you start with a shock and then you deny the crisis and then you get anger and then later on you go through the depression and then from there you can do a restart or a new start so we have different phases of the crisis and that's what we're experiencing right now in Germany. We are kind of in the phase of denying now after six or seven weeks of being in a shock and now a lot of people are in this kind of mode of well nothing happened everything is okay we don't need coaching no resilience it's not a topic you know this is exactly happening you can really nice to see how all the curve is now walking around these different phases of crisis and at the same time I know a lot of people who don't experience a real crisis so that's really a very interesting phenomena I can see right now I'm teaching resilience now since over 12 years and what we can see people who are very well trained in resilience or give resilience trainings they have much more capacities to be in with these days also people who do improve for a long time so this is such a benefit for people have these skills to manage or to deal with the unexpected things now and to have your improvisational skills really awake from this phase. Thanks for that. What I'm hearing in some ways is the way you've described the cycle of crisis also sounds like the cycle of grief that that people often go through and that people are in different places in that cycle and one of the things I'm seeing is people somehow feeling like there's something wrong with them if they're not further along you know and that sounds to me like part of the work is supporting people wherever they are which is also a very foundation improvisational principle I'm wondering if you can give us sort of your definition of resilience or what are the what are the quality of resilience that you would identify? Yeah so when when I work with resilience it's a very simple definition it's the quality or it's the capacity of tolerance you have when you deal with pressure or when you deal with something that is you know we say it's a window of tolerance so your system so it's the homoestasis of your nervous system and so when you are stressed the subparticles is becoming active and so you go into this quiet or freeze mode and after this acting this stress out then normally you go into a mode of relaxation and the power of some particles goes down the vagus now becomes active so and then you find a good homoestasis around this and and here is the window of tolerance that we call the resilience and the resilience can be small or it can be bigger to tolerate a stress and this is one once one possibility to define or keep a definition for resilience and this is one that's important for me when I when I work in the field of health when I work in the field of innovation or culture then the definition of resilience is a little bit different but this is the principle of you have a situation where where where the where you have pressure and the system and the system is able after the pressure to bounce back into the normal state and from when I see it from the theoretical perspective of a model I have this axis of change and stability and resilience is the capacity in the middle that you find a situative balance between change and stability change and stability or edge in you know you have your edge agility in the system you are flexible you can move you can you know your body can can be very flexible and adaptable and on the other side you need stability your system has form has culture and this is the real-time learning in between these fields of stability and agility that's my definition of resilience and the moment yeah thank you and what I what I'm understanding from what you're saying is that it's physical it's psychological intellectual right that it's something that we process on on many levels exactly yeah so the interdisciplinary applied research around resilience this is really a very wide range so your patient system for example you talk about resilience the brain is a part of your resilience capacity to how do you say it's the capacity of restructuring your brain after an injury for example the nervous system is a very important part and so it's always a combination between physical and psychological and also personality personality also very important aspect of resilience because every person is working differently and have different personal of psychological needs and when these needs are not served then everybody is working differently to stress or things that are stressful for you can be great for me you know I can experience this right now in the crisis of in this corona crisis I know so many people who are really flourishing at this time right now it's unbelievable you know other people shut down you know people really need to be very active with other people need to be interactive and need a lot of social contact they are suffering so much and walk by people who like to be alone more intellectual people know what to do you know they use the time for reorganizing their lives so it's so different how people cope with this situation right right right and and that speaks to some of what I was thinking about before which is you know it's it's a fairly human phenomenon to compare our experiences right and for the people who are struggling seeing all the people who are thriving it can add to a sense of you know disease because you know I've heard a lot of people kind of what's wrong with me why can't I write great you know the great novel I've been wanting to write all this time and that frame you offer between stability and change is really quite significant right now because we've all had to change very quickly and for a lot of people change is very active and stability may be very fragile which is why you know I think we are in what we would call a collective crisis does that yeah because we had you know we have for statistics from from our diagnostics so we're working with a diagnostic diagnostic tool and from there we can see that for example my baby blood generation we have more people in our German culture also in the German town are more intellectual and value-oriented and more in their brains from from nature you know when they wake up in the morning they're first in the brain and then later they go into the body and feeling and into the emotions and they become social so they're different ways of experiencing the world and in Germany we have a lot of high intellectual analytical people for a high value-oriented because we grew up in a time where everything was predictable we are in quality so looking for the details looking for structure we are architects we design in a way of engineers you know that's very funny to see and I work in a company and we see in the statistics a lot of people with this high value or analytical skills they need a lot of safety then a lot of planning then a lot of structure or good information to feel safe you know to feel positive to feel resilient about what's going on and right now when these people don't have these informations anymore and you don't have anybody who gives you direction or orientation and or enough space or time to collect the information and structure it and these people are so stressed and in the last 10 years where the book about becomes more more or a topic also in our business world these people are really freaking out because 20 years ago to be good and to be successful at work they had a lot of time they could go in details they could really enjoy the way they wanted to work and these days notice a 70% is okay work agile and then iterate from there and to some groups and you know and they say no no no I can't do that you know I have to have to dive deep deep into into information and and on the other side when I work for a startup then we have a lot of creative active people who like to change they are looking for inspiration all the time you know a lot of input people are high active and and creative and so it can't be crazy enough for them to be to be happy you know and and to improvise and to be with the unknown the whole time and since we have this data it's it's much more easier for us to see what's the culture we're working in how much improvisational culture do we have other people happy with the way we are in because there are also different styles of input to improvise and that makes it for us much easier to to connect psychological needs also to what people need to be feel safe and and to be strong and also to have their kind of personal way to improvise that's very different for person yeah yeah I just want to make sure people know what you mean when you say wooka world so the volatile uncertain complex ambiguous world is the term wooka and also for people who don't know that was the theme of our applied improvisation network conference in Berlin in what year was that 2013 2013 where you were the one of the co-hosts of that conference so thank you many years later for that beautiful effort I know it's hard to believe it's been that long so what kinds of things are you thinking people can do right now to strengthen their resilience because resilience isn't something you either have or you don't right resilience is something you can build you can develop yeah so what kinds of things can people be doing right now to strengthen their resilience during these times yeah so from the from the point of the nervous system the first thing you should always do is what we do right now so reach out for people find ways to connect and when you connect find ways to connect with an option of have a picture the visual connection to another person because the nervous system needs visual signs of a smile eyes even if it be with you don't have to have to make a little bit like this so that I can see your mouth and your eyes and your how do you call this wrinkles the creases the creases very important to have or talks is not not not helping at this point so and so this is really very very important as you can purchase I made a great video a few weeks ago in March and and he was really pointing out reach out for people and even if you just can hear a voice that can be beautiful also because the voice gives us also a feeling of being connected be in a state of social right now because when you have a lot of stress and you really really good in self-regulation then it's much in these days for you but not everybody has this capacity for self-regulation all the time the most people in our society are meeting the correlation and correlation as we need to calm down to calm down the stress and this is one of the most important things reach out and the next thing what you can do is create rituals so this is also what gives your day a structure more fine more stability to kind of sorry more stability yeah well when the book of worlds like this then then you need to to look for where's form where structure little things that he over the day so find some things you like to do and what's good for you but do it regularly find a rhythm to do it and so slow down the super improvisation of become a little more structured so that that can really help and this gives gives a lot of safety another thing I would I would recommend is see that there is a good body and brain connection so especially when you at home it's there about that that you stay connected to your body because when you just go into your brain and you're always sitting on in front of the computer or just laying down or watching TV or something from there when the when the system is not really opening up so when you just pull under your bed all the time then the psychological system will go down a little bit so what I can recommend is to some power-posing in between you know have this yes and gestures try to open up yeah just stay in the room for one or two minutes open open open your arms to a little bit she gone or to some some exercises to some Joe yoga it's ten minutes a day five minutes a day that's enough but if your system every day a little bit open up look look that also the whole just in principle inside that it can wake up every day for a few minutes so that gives you a little bit more better homo status of your home your hormones hormones hormones and hormones yeah yeah home and these are little little things but it's it's also to you told me today before you you go regularly for walk outside with your dog you know it's great when you have a little patch so that helps you to stay in motion so stay in motion go and go to the internet reach out for one of these dancing groups for example you know dance in the kitchen do something you know but don't forget your body it's so important that you stay connected to the whole system and yeah stay connected also with fun and play this is one of the most important things say it is see that the nervous system is really has its play times I don't know how it is in in America but we have so many beautiful improv sessions online you can do improv every day nearly it's beautiful you find people to play with you find people to talk with doing funny exercises and and I think this right now is a good time to just have to also for fun you know we do a lot of applied improv with various areas but I think I recommend in these days just to just play into something regularly this is just the and then basic needs are coming you know food drink and take care of all the stuff around yeah when there's too much stress you know what's happening drinking smoking whatever is your your little your little whole would you say it in English compensation oh yeah you know and just sometimes just we regulate yourself and then wait one or two minutes till you take the next cake or take the next shop work or take the next trip so bring time into the system when you when you have these times you have a lot of experience of impact you know it's very tight the system is tight yes a lot of fear and whatever is happening to us just always like give space open up and give time and it's like this is a basic work which you can do also in trauma just give your give yourself more space this is very very important and sometimes when you really have a panic attack or something is happening to the basics like I don't know if you know so some tapping techniques so basic type of techniques or what's very you know something that is we offer the stuff the stuff of this exercise we have regular online meetings where we where we do these stuff with people so they can go online and as a friend of mine she's doing a lot of people work also or doing this tapping regularly every second day she has a course and a very simple things also like you know being context just feel here I'm here I'm there call things by name you know what when you release to the rest of your elbow finger nose you know here it's it's about orientation this is what we do when we when we are doing improv a lot you know we find in cop orientation it's so important to know who I am where I am what do I feel okay where am I okay here's my finger here's my nail you know like bringing your consciousness into the moment is so important because the brain these days when you get fear or stress it's running away and you go into your fear and your fantasies of what can happen and then you are not here anymore so everything that helps you to orient yourself play improv with yourself you know play I'm a tree and I'm the bird of the tree and I'm the I'm the son on the bird that is on the tree or something you know play with yourself and whatever so to improve and but just something that gives you the moment of mindful respect so at the moment for the moment yeah yeah so helpful I and you know as we look at the cause of trauma and challenge being physiological emotional psychological intellectual spiritual then then the remedies have to also be in all of those claims so the physical the relational all the different ways we can bring ourselves back and I I'm thinking a lot about the really important improv principle of being here focused in the moment and seeing what's next because I think a lot of the anxiety that people are carrying is about you know the future and that's really anxiety is about the future and so all the things you're talking about are helping us to be in the present now in this moment now and strengthen our kind of internal support for that yeah so basic inner work this is now the time for inner work and to really find all these connections there's a lot of stuff more what you can do intellectually but I wouldn't recognize recommend first like all this intellectual coaching exercises like right yeah you can do that right down few things that went well today you know all the stuff we have these in books you know everybody has a helping self-help book in the shelf but you can all but what's much more important than just starting intellectually working with the brain is start with body yeah so important connect to reconnect the system to it now yeah yes so I'm wondering if there's any kind of short improv activity that you would do with me right now that would be an example of something we could do to strengthen our resilience yeah we can we can do maybe we can do a little we can do a little combination between a power pose and storytelling okay great yeah that's a very simple thing I do with clients a lot so how are you start we can see so maybe we are let's say we are in a in a store or something you know and and you bought something that was really really you were not happy with what you bought okay so I should slice her and you're very angry and very tight no and then now always when I say oh let me check this and I put this paper here then this is a sign for you to put your hands behind find the reason to lay back and then try to be angry okay okay and see what's great hello hi how can I help you well I'm very upset I bought this milk and I've been needing this milk and it's sour and I can't use it in my coffee and there's no other milk in the store that's so interesting so I like that down so milk is so can you tell me a little bit more about what happened so when did you buy the milk I bought it yesterday so what was the experience when you bought the milk how was it here in the store just say well I mean everybody was very nice and I really was looking forward to the milk because I had milk at home yeah yeah who helped you to get the milk was it my colleague or who helped you with that yeah was this guy named Jim yeah he's a very nice guy yeah yeah yeah he has two little kids it's very beautiful so that the kids sometimes come to the store and then he's playing with the kids and the milk and so that's so nice so yeah so what what happened then I went home well so I was so excited to have coffee with milk which I haven't had in weeks because I haven't been able to find milk and then I poured it and it was sour and after all this time of waiting to have milk in my coffee I couldn't I couldn't have milk in my coffee did you maybe put the milk into the sun or something so that it no sure no I did not milk in the sun are you saying it's my fault no no no no I'm just exploring a little bit what happened in detail you know because it's very important that I make these notes so I can I can go to the to the person who I got the milk from so to see if we have more problems with other milk yeah we don't want anyone else to have this problem yeah so how do you feel when you when you do this how long can you stay angry it's very hard you know I mean like I feel like I'm on a like you know a Caribbean island relaxing it's very hard to be angry even when I was trying to be I was smiling I noticed yeah so it's how I do this a lot with my clients you know it's a very simple improv exercise like this when you bring stuff back and you have these conversations and normally they they go into anger anger anger and then you have this funny conversation but when you give these signs of relaxation then it's when you do it for one or two minutes and then the people try to stay angry it's so fun yeah and it's possible you know and this is what what you can do for example when it's about so what's happening with my life and the corona crisis how many people will become ill when you maybe have this conversation also online with people who are really freaking out just give them you know that there are different possibilities you know this is a little provocative when you just you know somebody's telling you and then you make like this but but it's like back a little bit yeah for example you know you can you can do also do like this or really nice put your legs on the on the table to like this you know make it in little steps step by step and then from here very slowly and then after two or three minutes go into this and you will see the other person go lonely relax and relax and then you know yeah yeah that makes a big difference you know when you're sitting here in front of a zoom and you always know when you say okay I can right now not intellectually reach for the person because he's so stressed but when you are good self regulated then you can open this your own resilience and you can your own resilience and self-regulation to the other person then you can co-regulate and that's not and that's a very easy little technique to calm down yourself relax yourself and then give this big invitation for the other person also to change the way you're talking about things yeah part of what I'm taking away also is that in this absence of our physical ability to connect with each other that it's more and more important for us to physically connect with ourselves so that my ability to relate to you even through the screen is based on a groundedness and a connection I know I'm struggling with the desire to connect with people and the overwhelmingness I'm feeling about so much screen time so sometimes I feel like I have to choose between connecting and having my brain explode and so this kind of work you know keeping me grounded physically it's really important to allow you to maintain connection yeah yeah and also experiment a little bit with the way standing sitting change positions but I sometimes do I just change the higher you know that also I'm I have from one conversation to the next different different angles my system always seems to be small you know it's these are little things but the body's record in these days you know when we really want to solve this problem of stress and stay with it we have to work with body that's really the most important thing and the connection and have have a good connection you know eye contact and and take care of what the voice for example when you would talk to somebody and your nervous system is recognizing that the person is maybe to pass all the time and all the time and talking and talking and talking and you know that's a it's we call this is over coupling so then you should never listen longer than maybe half a minute and I see or he was say oh hey hey clouds that's a cool thing what you said like and then interrupt you know because then the people normally go into the story and of the past of the stress and then bring them back to the moment and say oh yeah yeah I can understand that that was very stressful yesterday how's it today tell me how's it now tell me a little about how what what you are experiencing now in the moment you know this is really bring in this improv mindset again from here now because then they have to step out of the spiral when you very nice very polite and you listening five minutes somebody's going into the spiral then you go into the spiral yes and then worry goes into viral right you know and both what we but we have to be very professional in these days with us with ourselves well one of the things that helped when I was doing this was also your voice I mean you were very even very soothing very calm very positive so you were listening to me but you weren't hooking into my anger right you were you were helping me go forward in on a different path is how I felt and so I think also the relational quality of what we can do for each other during stressful times is to provide some of that calming response pattern yeah from the input point of view I switched into the mode of tell me more go more in details you know I it's not advanced it's more detail expand the color so yeah yeah so beautiful yeah well I could talk to you all day but I know it's nighttime there and I want to respect your time and I have a feeling we'll have more to to bring you in and thank you so much for the time and I'm glad you're staying safe and I know Germany has slowly reopened so we'll be watching to see what happens there and whether it's during this crisis or not your skills and your knowledge are very valuable I know you've written books on resilience and I'm waiting for the English translation of it and yeah yeah it's a start it's wonderful to see you yeah thank you so much thank you so much for our room by playing with me that was so nice so from burning Germany we will I okay bye bye bye bye


Hello and welcome to the CSC 316. I'm your instructor Adam Guita. You can call me Mr. Guita, Mr. G, Adam. I honestly don't really care. I don't, I look at it as pretty much, you know, when you go out into the real world, you don't typically call your boss, like, mister, doctor if they're a doctor. So just kind of freely call me however you like. For our class, we will be using the sixth edition, Data Structures and Algorithms Wiley book. Fifth edition is fine. Really kind of the meat and potatoes of this is, this is stuff that even I learned way back in the day, you know, I actually recommend definitely getting this book and keeping it. Don't don't sell this back for like pennies. And the reason why is because, you know, yeah, programming languages can change. You know, I learned Java third edition when I was in school, where almost about to get Java nine. I then work in different languages, JavaScript, Python, SQL. So, you know, languages can change. But the important thing is something like this book.  And that's actually going to be one of the more interesting things about this class, I think, is because in say 116, 216, you've spent time, you've learned computer science, you've learned a lot of programming. The syntax is still kind of freaky. In this class, we go, okay, you know how to do that stuff, you can compile a program, you can you can do critical thinking. Let's actually look at that for a second. And let's see if we're doing everything correctly efficiently. Think, for example, to a dictionary, a traditional, literal, this thing, big book thing that I got to flip through. Well, if I want to look at something, say, in the Jays just, you know, Java, I don't start literally page one, page two, still haven't found my Jays page three, page four, I don't do that. We have techniques that we as people do. Oh, I just happened to maybe I open the book in a specific way, because I know Jays are kind of in the middle of the alphabet. And so now I can do sort of a pseudo by sorting method, excuse me, a sort of search. And so this allows us to do things a little bit more efficiently. So now we actually look at that and go, well, if this is what I did is to make that more efficient to search for my my Java in a dictionary. Can we do that with the computer? And can we do that with our computer programs? So what we're going to do in this semester is we're going to start to look at, are there better ways to do some types of programs, some types of problems, introduce those sort of solutions and again, some of the different concepts that will transcend time. What's really important is this is honestly the class that all your job interviews are going to just like sneak in. They're going to be like, can you do a balanced tree? Can you do you know what red black trees are? Because it's the theory behind it. Amazon needs to know this stuff because they have millions and millions of products and that becomes a big issue. The bigger the number, the harder and slower a computer can go. And so however we can make that much more faster, much more efficient is better. So welcome to class. I'll see you guys in the class. You'll see a few of these shots. This is just going to meet my apartment. I'll do a few with a green screen that way I can kind of interact behind there, but you should see expect these videos as well. I like to think about that as just kind of a way that way if you forget something or can't make class because it's the summer and the beach. You can at least still come and you can still watch these videos, pick up on things you may have forgot or miss while you were listening to me the first time or hooky. You paid for this class. So anyways, see you in class.


So today what we're going to do is we are going to, you'll notice there's no demo equipment today because today is We're going to just dig our hands into the guts of the cadaver that is calculus and just do it We're going to own it today. All right, so we are So we're going to solve problems involving complex distributions of charge That's going to be our task today, and I will attempt to demonstrate in itty-bitty steps how to do this I hope I will instill in you two things one not be afraid to look stuff up That is okay. Just tell me what you did. I used Wolfram Alpha to do this interval I looked in wikipedia and got this number just write your source down Okay, just say what you did in science. You don't have to reinvent the wheel every time you want to do something complicated You just have to see if anyone else has done it before and acknowledge those okay, and then just go ahead and use the Results so I want to drill that into you of course I expect you to be able to set up and solve problems. That's a life skill But you know the details of how you get that final number grinding through some hypergeometric function that you have to integrate I promise I'm not going to make you do that. I promise. Okay, those are all we make grad students do those and they hate us for it That's been solved. Okay, probably like 13 Russians 40 years ago went into Siberia and figured out for you So you don't have to do it anymore. Okay, somebody has done it All right, there are lots of smart people in the history of the world and we have books full of their information All right, we should use it and you should learn to use it and not be afraid to use it as long as you say what you did So let's go over the concepts again that we've kind of touched on so far These are the core ideas. We've walked away with it all fits on a slide. Okay? There are two kinds of electric charge positive and negative they exert forces on each other Positive negative electric charges are the sources or recipients of electric fields So by convention electric fields emanate from positive charges and they go into negative charges Okay, that's our picture and that's how we describe nature involving charges present in nature. It works very well Okay, electric fields and forces are vectors. That's because they have both a magnitude and a direction We saw that kind of dramatically last time with the Vendagraph generator I had that little piece of Mylar in my hand and as I moved it around the tip of the Mylar just kept pointing at that sphere Okay, you can really see the vector nature of the force there There's a direction and a magnitude to this thing So we describe it using an mathematical object called a vector to find the total electric field or electric force We add as vectors the electric fields or forces due to the individual charges So imagine you have ten charges, okay that you can do that by hand That's awful, but you can do it by hand to get the total force that the other nine exert on the tenth You would sum up the forces from the other nine on that one So you calculate the force of one on ten two on ten three on ten four on ten and so forth So you wind up getting a sum from I equals one to nine of the forces the Coulomb forces of each charge on that 10th one and similarly if you just take the 10th away and ask what's the electric field at the point where the 10th charge was Due to all the other nine charges again You would just write down the little point Coulomb electric field equation and you'd sum those up as vectors And you get a big vector at the end. Okay, we have magnitude. We have direction All right any questions on those concepts. We're going to exercise this more today. All right All right, so so let's do some announcements. So you're next assignment for class You're going to keep reading chapter 22. I think we're going to finish it out. We're going to start talking about The actual Effects that forces have on charges electric forces have on charges We're going to start throwing f equals ma into the next we're going to start looking at velocity and acceleration We're going to do all that 1307 stuff, but now we're going to use this force to do it Okay, you had a little sneak preview of that with the uranium nuclear Nucleus decay in the first homework problem set. Okay, we're going to build on that And one of the things we'll do is I introduced in the lecture video this thing called the electric dipole That's just fancy talk for I have a positive charge. I have a negative charge They have the same magnitude in the separated by some distance. Okay, so that's what a dipole is okay two poles dipole So one pole another pole equal magnitude charges opposite sign separated by distance.  Okay, so I gave the example in the video of The alveoli and the little layer of water that fills those sacks in your lungs And if you don't have a surfactant in your lungs to lower surface tension the dipole force in the molecules of water on the Surface of that thin layer are enough to prevent an infant from taking its first breath So as long as we collapse it would not be able to reinflate the dipole force is that strong and we have to secrete a chemical called a surfactant to overcome that Prematurely born infants don't have that so if you're born six seven eight weeks premature or more You do not naturally produce the surfactant It's one of the last things that's made by the body before you're born So artificial surfactant has been around for decades and it's simply sprayed into the lungs when the infant is born So that they can reinflate their lungs after they take after they exhale their first breath Okay, so it's not the inhale That's the problem. It's that first cry and then they can't reinflate their lungs and that's really bad Okay, so premature infant several kinds of issues physics plays a role and probably all of them in some way or another and specifically in this case the dipole force plays a significant role in your Chance of survival three seconds after you're born okay You have to overcome that dipole force the body has a way of doing that But if you're born too early, it's not ready yet and you can't so thankfully medicine has a way to overcome that We've learned how to do that. All right Okay, so this actually this statement here Well, we'll get to this one for his homework to is assigned today should already be up on Wiley You should have an electronic copy of it again. Look at your numbers in Wiley plus It's off the website and there is a problem again that I wrote myself tacked on to the end and I want you to Hand in solutions to that one too. Okay That's again doing a week Now here's the start point teams are final star as of today So starting tomorrow what I want you to start doing is meeting with your team once per week outside of class But I had to do a little last-minute reshuffle. We had a late drop in the class and There's been some consternation expressed about their late last reshuffle So I'll probably move people back around again. So I think it's teams Delta and Echo You'll be getting more emails from me. Okay, so we'll sort that all out so people are happy So let me let me say this if there's anybody on team Echo that wouldn't bind mind being moved to a different team Email me that will make my job a whole lot easier. Okay, so team Echo was the big one But we had a drop from another team I'd like to kind of get the teams all equally sized at the beginning of the of the course Of course, I can't predict future changes, of course But if anyone on team Echo would like to be moved to team Delta or wouldn't mind being moved to team To team Delta I gotta move somebody so just let me know that you know, oh, I don't care. It's fine. I'm cool Whatever I'll do whatever you tell me. I'm you know sheeple. It's fine. So all right So your job remember your homework for next week next Tuesday is just to select a team name. Oh, yeah, Sophie Yeah, I what I'm gonna do today is I'm gonna email all the teams so that everyone has everyone's email address. Yeah Yes, so I will comment next week on team dynamics and Leadership and then we'll address some issues about people who are contributing and people who are not contributing and we'll talk a little bit about that Okay, all right, because you know, we're all human beings. We all commit different levels of things to activities It's fine to get it, but I gotta give the teams a way of dealing with this, right? So So you're gonna select a team name remember the guidelines. I'm gonna urban dictionary things I don't recognize email it to me and everybody on the team has to agree So whoever emails it to me is see seeing all the other members of the team I'll get you your email lists for your teams today. I Want when you meet okay, so some time between now and next Friday you're gonna meet as a team in person face-to-face And what I want you to just chat about is how does anything you've learned in this class or even the previous class inform? One idea one avenue of a solution That you could apply to the grand challenge problem. Okay, that's it That's all I want you to do in your first meeting and if you come up with nothing No problem. You got other meetings and we're gonna talk as a team to mentor Kind of thing at the end of September. Okay Any questions? No, okay. Well, then let's do quizzing so that we can get to Nothing Okay So We're gonna check a claim At the beginning here But let's go through the quiz questions first and discuss the the answers to those so let's look at the first one as Mentioned in the video lecture. What is the approximate typical number of charges in a macroscopic a human scale something in this room? Blob matter. Okay, is it one a million? Okay, two a billion Three whatever the bad number is But really I have no idea what that is. I just wrote it down four of a God knows number Okay. Yeah, all right. So many of you went for a God knows number and yeah, that's the number And I think I think I actually I put it wrong in the video I think it's 6.5 times in the 23 in the video So I'm gonna have to go in and do some careful video editing on that one and re-upload that YouTube video But that ain't happening anytime soon. So I promise you that's the correct number if I did say 10 to the 23 I apologize and you know what? Yep, this is the jar. This is the famous error jar. I owe $4 into this now. I already put one in and took one off the I owe you last week Oh my lord, okay, so that's the mistake either way you're getting a buck out of this So I'll fix that in the thing. Okay So in that case then we'll just have to correct by factor of 10 something I write on a later slide No problem. I should really not second-guess myself at 730 in the morning. That's a bad tactic So I'm gonna recommend everybody just sleep past 730 in the morning and don't do what I do get up early Okay, good. Yeah, I've got at least one take around that. All right. Good. All right So that will get fixed and I will not have to do any careful editing in the YouTube video And if this is all recorded so all my colleagues can see why I showed up my PhD taken away from it All right, so question two, which of these is a true statement about the electric dipole moment? One it's total magnitude is given by the magnitude of either charge q in the dipole takers for one To its total magnitude is given by the separation d between the two charges takers for two Three it points from the positive charge to the negative charge with magnitude qd q times d and takers for three Okay, and four it points from the negative charge to the positive charge with magnitude q times d Lots of takers for that. Yeah indeed group think worked here as well All right, so it's number four. It's um it falls out of the derivation But the convention if you just want to memorize it is that this is one of the weird things where something starts on a negative Goes to a positive dipole moments you start in a negative charge and go to the positive charge And that's that p vector which is equal to q times d vector and d just points from the negative charge to the positive charge in the problem, okay All right So how do we determine the electric field of an arbitrarily shaped large number of charges one? We always do the sum by hand putting in one term for each charge even if this takes forever No one's going to jump on that one. Okay, all right to we utilize integral calculus to perform a large sum more quickly Few people all right fine three. We can always just use Coulomb's law for the electric field and stick in the total charge q No one fell for that. Okay for we can't there's no known way to handle large numbers of charges. Oh, thank God Okay, good. All right. Yeah, it's two. We're going to use integral calculus. In fact, we're going to exercise that today Okay All right now I made a claim which I've misstated and then restated correctly Thanks to help from all of you and that is that this Apogadro's number has something to do with sort of terrestrially scaled things All right, so so let's kind of test that claim a little bit right at the beginning All right, so we're going to solve problems first of all involving Complex charge distributions. That's our goal for today and I'll demonstrate how to set up and solve a Basic problem along this line and I'll give you a variation on that problem to try to do yourself. Okay So let's talk about copper. All right, let's you know, we're thinking about matter We're thinking about charges, you know copper is made of copper atoms We know that now thanks to hundreds of years of study of matter You know, this is a actually a very quite lovely picture of lots of copper wire laying around in little spools Okay, a little copper tubing something like that So each of these is you know a few meters long and and you know a few maybe 10 millimeters in diameter something like that It's pretty much solid copper for the most part. So it's it's fairly pure copper Coppers quite valuable as a commodity these days Well during the housing bust When houses were abandoned one of the most common things that was stolen from abandoned homes There's copper wiring and copper piping because if you sell that for scrap on the black market or really any market Just to scrap you can make a lot of money very quickly Copper is very valuable per unit, you know mass basically it's because we need it so much for Electrical devices these days it's so commonly used everywhere in computers and wall wiring and plumbing because of its thermal conductivity Which is very much related to its electrical conductivity. It's a very valuable metal. All right so if If you have some net charge big cue that's deposited on the copper wire or copper is a very very good conductor So if you put free charges onto neutral copper They will be free to move anywhere they want in the copper material And they'll kind of move until they come to an equilibrium place where all the charges are equally pushing on one another And they can't move anymore, and they stop so you have to wait a little bit Maybe a billionth of a second or a millionth of a second or something like that But eventually the charges will settle out an equilibrium and they'll be distributed over the copper Primarily on the surface, and then they'll just stop moving they can't leave the copper But they can move freely on it or through it, and they'll do that until they come to equilibrium Now that charge cue that we've deposited on here It could be made from some huge number of elementary point charges, and you know remember the elementary charge is about 1.6 times 10 to the minus 19 coulombs, which is a tiny number Okay Now are there really typically like Avogadro's number or thereabouts of like atoms and charges just in stuff That we find around us all the time so this morning using the wrong number for Avogadro's number It was we'll correct that in a second. I went and check that out. Okay. I mean I've checked this before I've done it a variety of ways this will come up again in the course later with an exercise we do later on But you can just check this you can you know back to the envelope very quickly on a small piece of paper Kind of look up some numbers and work out is this true All right, so as the famous physicist Richard Feynman once said shut up and calculate if you want to answer this question Just get some numbers and do some math. All right, so let's get some numbers and do some math All right, so let's consider a lamp cord right typical cord, you know much like this camera Cable here. It's got some braided copper wire inside of it That's used to carry information from the camera back to the device and actually some information from the Device back to the camera because there's a little light on there that comes on when it's recording and so forth. Okay Now, you know imagine that the typical lamp cord is something like I don't know a couple of meters long So I said two for the purposes of this problem I just pulled these numbers out of nowhere this morning. Okay, and it's entirely made from copper metal keep this nice and simple It's pure copper So the typical thickness of like an electrical cord and you can look this up if you want on the internet But in the United States we use something called the American wire gauge Which is a bunch of standard numbers that represent diameter thicknesses of wire and it's a very standard thickness for house wiring is 14 AWG American wire gauge and that corresponds to a roughly 1.6 to 8 millimeter diameter All right So house wiring if you were to you know got the walls here and look at the electrical cables behind the wall You'll find that the majority of them in this building are 14 AWG We'll figure out why that is a little bit down the line with some homework But that's a very standard number in American construction and you'll see why later. Okay, it actually has a physics reason for that Now the density of copper is 8.96 grams per centimeter cubed at standard temperature and pressure Do you think I just know that number off the top of my head? No good Weston, right? Yeah So how do you think I got that number? I googled it That's exactly right, and I found Wikipedia and Wikipedia told me the number Okay, you know Wikipedia can be wrong for some some political things, but for like science things. It's basically pretty solid So don't be afraid to use Wikipedia to look up basic information about the cosmos like the density of copper There's not a lot of debate about that anymore in our society. Okay, because you can you know measure it and stuff All right, so I just looked that number up Of course that probably needs to be converted to kilograms per meter cubed And I think if you do that it comes out to 89 60 kilograms per meter cubed. Okay, so it's pretty heavy It's a lot of kilograms for a meter cube the copper copper is not white Okay, if you've ever tried to pick up any significant amount of copper, you'll know that okay, so We've got a density, but we want to get a mass and once we have a mass if we know the mass of a copper atom We can figure out how many copper atoms are in that cord So we got to get the volume of the cord. We got to use that with the density to get the mass of the cord Okay, so the volume of the cord if we just Approximated as a long two-meter cylinder with a cross-sectional area of radius one half the diameter You can plug in numbers and solve so volume will be area times length and That's for a perfect circle going to be pi r squared times l and then if you plug in the numbers You should get if I did this right four point one six times ten of the minus six meters cubed so a teeny tiny volume Not a big surprise. It's a very thin cord. It's long, but it's very small. Okay, so it's small in meters cubed I mean a cubic meter is you know big, right? The neck cord doesn't fill a cubic meter. Okay All right So we have that and we have that the total mass then of the copper metal is just the density which is Kilograms per meter cubed times meters cubed will give us the mass of that cable And we find out that the mass of that cable is about you know 37 grams so 0.0373 kilograms So not that heavy, but you'd be able to feel that in your hands. Okay All right, so carrying that number with us on to the next salt slide So that's just repeating when I wrote on the last slide right there We can keep going if we want to find the total number of copper atoms in this cable We've got to divide by the mass of an individual copper atom and that will give us the total number All right, so the mass of a single copper atom is sixty three point five four six atomic mass units or am you? Now did you know you can do numerical conversions on Google? How many people knew that? Okay a lot actually yeah, so you just you can even talk it into Google, but I just typed it I said sixty three point five four six am you in kg and it converts immediately to one point oh five five times ten of the Minus 25 kilograms so what Google has done is behind the scenes they're running a program called units UNITS It's a standard program on the Linux or macOS Unix operating system So if you have a Mac computer and you pop up a terminal and type units you'll get a little prompt And it'll say what do you want? What do you have and what do you want? And you can convert just about anything to anything else and if you try to convert like meters cubed to meters squared It will tell you what the correct conversion factor is to handle that okay. It's pretty cool And it's got hundreds if not thousands of units that you can transform So if you need to get from one unit to another and you don't trust yourself going from centimeters cubed to meters cubed in Your head or even on a piece of paper check it with units and see what you get okay? Check it with Google and see what you get All right, so so that's the number I got then if I just divide the mass of the wire with a mass of a single copper atom I find out that I have three point five times ten to the twenty three copper atoms Which is within a factor of two Or thereabouts of Avogadro's number right correct me if I'm wrong six point oh two times Yeah, you're not in your head Western because you know such on such an idiot that I screwed that up This is good. All right. Yeah, so that's within about a factor of two six point oh two times ten to the twenty third Which is Avogadro's number I learned today Okay So I said 20 here because I'm a moron and I'll fix that in the slides before I upload them all right All right, so that ain't bad for approximating factor or two You know for that many things in something we just kind of winged it on in terms of I just went for two meters long It's got 14 AWG. Here's the mass of a copper atom go to town. Okay So if you then ask well fine great So how many charges are in there how many electrons or how many protons you can look that up in wikipedia to a stable copper has 29 electrons and 29 protons so the Yeah, I think that's right the total number of electrons. I really shouldn't do things before eight in the morning a Total number of electrons or protons then was just 29 times the number of copper atoms and that comes out to be one ten to the 25 Okay, and that's a factor of that's again within a factor of about 20 or so of Avogadro's number, so that's pretty good for this kind of quick quick work So when somebody asks you how many atoms are in that table you can just say what about Avogadro's number? How many atoms are in that bottle about Avogadro's number? It's basically right to within some factor of 10 or 20 or two or three or something like that I mean you basically be right and that's just because we're Macroscopically sized in this number is meant to represent the rough number of atoms in a Macroscopically sized objects that no accident. Okay by the way that Avogadro's number is defined All right, so that claim kind of holds some water All right, and we can use that especially going forward if we're going to estimate things if somebody Asked you to estimate something about a piece of material and you don't know how much stuff is in it You can just wing out Avogadro's number and go from there and just say look I assumed Avogadro's number We can correct that later if I'm wrong All right, so what happens if you have Avogadro's number worth of charges that you have to add up and get an electric field for that's the problem We're going to tackle today, and we're going to do it using integral calculus integral calculus is just a shortcut trick using the basic ideas of calculus to Divide up a problem into many many equally sized small pieces Add them all up send the piece size to zero and see if you get a finite result a non infinite or non zero result when you're done Okay, so what we're going to do is we are going to look at sort of a lamp cord problem again All right, so now imagine I have a bear lamp cord the copper is just exposed and I it's infinite in length All right, and so why do I get to do nonsense like that? Why do I get to say infinite? Well, you can approximate very long things especially if the scale of everything else in the problem is teeny tiny compared to it You can approximate the size of the big thing as infinity and see what kind of answer you get and then later on if somebody says well There's no such thing as infinity in nature at least not that we've really encountered so far, so Really, it's finite in size. What happens if you assume it's actually finite in length It's only 10 meters long instead of infinity long well as long as the the problem You were originally kind of considering how to small scale in a big scale and that big scale is way bigger than the small one You'll find out that the corrections to your assumption are fairly tiny less maybe less than a percent level So who cares at that point and why the plus won't even care at that point Okay, I won't care that you're off by tens of a percent it cares that you're off by a percent all right So calculus lets us Along with just sort of the basic tricks of mathematics the little toolkit of mathematics It lets us take a seemingly complicated problem bust it into many equally sized small pieces Add up all the pieces and get a result And if you tried to do this by hand, which you're welcome to try doing adding Avogadro's number worth of charges together If you try to do it by hand, you'd never solve the problem You can't count to Avogadro's number in your lifetime even if you count it as fast as you humanly possibly could okay, so Let's see if we can tackle a problem that involves a large number of charges and throw calculus at the problem and try to make progress That way so this is the picture We have deposited a charge q Uniformly on an infinitely long copper wire all right, so we throw this charge onto the copper wire We wait a moment. We let it all settle out into equilibrium So it's nice and uniformly distributed over this this shape this line this copper wire Okay, and now what we want to do is we want to just pick a point in space Call it P point P is going to come up all the time all right We're gonna pick point point P and we're gonna ask what is the electric field due to all that uniformly distributed charge at that point P All right Well if this was just a point charge with magnitude q located here, you'd know exactly what to do What would you do anyone anyone want to take a crack at that? Winston If you just had a point charge sitting below the point P and you wanted to get the electric field What would you bust out to do that? Coulomb's law yeah Coulomb's law now ask for points You always are going to use some some version of Coulomb's law and for the electric field I'll just jot this down here the electric field for a point charge is equal to k Times the charge of the point charge q over your distance from the point charge squared Times a unit vector that points from the charge q to where you are observing the electric field So that's Coulomb's law for the electric field It's very similar to the original Coulomb's law for force But we've divided out the second charge the one that would be sitting at point P the test charge Let's keep that in mind. Let's hold on to that equation. I'll leave it up on the board Okay, we're gonna we're gonna need that again in a moment We don't have a point charge We have a bunch of point charges of the Avogadro's number worth of them distributed Uniformly over this very thin copper wire Okay, so we're going to treat this copper wire as Infinitesimally thin that is it's only one dimensional it has no extent in the vertical direction or out of the page It only has extent in the horizontal direction. So we'll treat this as a perfect one dimensional thing Okay, an infinite straight line Now when you uniformly distribute charge over something you can ask well What's the density of charge per unit dimension of the problem? And the reason it's useful to do that is Because this is often a constant in problems that you'll get for this course Okay, so you can ask in this case because you have a line about the linear Charge density This is denoted by the Greek letter lambda lowercase lambda Okay, it kind of looks like a upside-down y and This is just equal to charge per unit length Okay, so it has units of Coulomb's per meter If you have a two-dimensional surface and you have a uniform charge density on that you have a surface Charge density then it's Coulomb's per meter squared if you have a volume It's Coulomb's per meter cubed and that's denoted by sigma the Greek little lowercase Greek letters. Sorry. That's a denote by row Sigma is the surface charge density All right, well we can ask since this is a uniformly distributed total charge q Over the length of this thing whatever it is. Okay, which we're going to approximate is infinite Let's for a moment just say that the length is some big number L whatever that is So I would write this as q over that big length L which later on I'm going to approximate is infinite.  I always get lambda for a line This is a helpful trick. This is how we're going to attack this problem later on This is how we're going to go from one little charge to understanding something about the whole distribution of charge Okay, so let's keep that in mind linear charge density is a constant no matter what scale we look at this problem Okay well, let's Let's go deeper Let me take a little section of the line here So this thing shoots off the positive infinity over the right. It shoots off the negative infinity over to the left okay, so I'm going to take a look at an infinitesimal tiny little piece of this So let's just kind of denote that as This thing here. All right, this little sort of shaded thing here All right, so this little thing here is an infinitesimally small piece of the line This is known as a differential Okay in calculus speak And it has a notation that goes with it If we are denoting this for instance Here as the x-axis, okay Well, let's put our line of copper with its charge on it on the x-axis The little piece of length here will be DX Now that's not D multiplied times X. It's a singular symbol and it means differential of X Okay So that's a single symbol now Sometimes you can manipulate these differentials like their for instance parts of a fraction People often get themselves into trouble with derivatives by thinking that like numerators and denominators will just cancel for no reason whatsoever There are rules With derivatives and there are rules with integrals that can often make the problem simplify as if it were Involving little fractions, but you have to be careful to use the rules before you just go blindly canceling things out, right? So if you see something like this DX over X do not do that. Don't say oh hey the X cancels out. I'm left with D Don't we're about to get into very bad territory at that point Okay, and then then I'll have to then we'll have to meet outside a class and figure out what your solution went Like that right afterward. Okay So treat that as a singular symbol a single unit.  We've zoomed in so far. We're looking at like a single charge Inside the matter inside the material That DQ represents a teeny tiny itsy-bitsy little point charge Right, maybe an elementary charge with size 1.6 times ten of the minus 19 or something like that.   I could add them all up and get the total I could do the superposition principle add up all the electric field as vectors get the total field Okay, that is our strategy That defines our strategy So let me begin by dropping some coordinates on the problem. Here's the y-axis We've already said that the line is the x-axis Okay, and I've decided to put the origin of my coordinate system straight below point P. So point P lies on the y-axis Let's keep going. We have a few more things we can draw here. All right So we're going to have an R vector That goes from the thing emitting the electric field to the place where we're measuring it That's the convention our vector our hat they point from the thing emitting the electric field To the thing to the place you're measuring that field All right, so let's just go ahead and draw an arrow There we go. That is the R vector for that little piece dq Just that one Does every piece on this line have the exact same R vector? Why not why not? Because they move right so some of those pieces are going to be really close to point P like the one dead dead underneath it That's going to be the closest any piece gets some of them are going to be really far away Okay, so that hypotenuse of that right triangle you can kind of see there the The height of it is the y The length of it is the x and there's the hypotenuse of the right triangle that hypotenuse is going to stretch as You change position Well, let's dig just an inch deeper into the ice on this one. Let's see what lies beneath What is it that changes when you pick a different charge on the line? Does the y coordinate change does the x coordinate change which is it Weston? Which do you think you think the x coordinate changes? Yeah, and you can you can kind of see that So if I pick another piece, let's say way over here Okay, and just for a moment I draw it's our vector I'm going to erase this in a second so we don't get confused We see that it still has a component whose height is still Why the distance of the point above the horizontal axis? But this x is different than this x so all that changes as you pick another Thing on the line is the x coordinate shifts This is helpful because it helps us think ahead that eventually what we're going to have to do is set up an integral Where we sum over x coordinates over the pieces in x y is going to be a constant y never changes Why should not be part of your integral? Okay, because y is a constant it never moves unless you change the point P Manually and move it here, but then all the y's are still the same for all the pieces All right So you're free later on once you get the answer to move y around you can make y 1 meter 2 meters half a centimeter Whatever, but for the purposes of the integral y doesn't change because when we're adding things up. We're adding things up only along x This is helpful.  It's due to the dq the dq is our squared distance away from the point P And there's an our hat vector for that dq that points from the charge to the point P The next step with a Coulomb's law problem once you've got your coordinate system set up and you've written down Coulomb's law is to do what what are we how we're going to attack this this formula? I just wrote down any ideas Plug in what we know. Okay. Do we know K? Yeah, it's a constant never changes, right? Now dq. Well, we just said dq is a piece of the line, okay, but We've also got ours and our hats and we don't know how to relate Like charge and distance so that eventually we have something consistent. We can sum over here I mean right now we're kind of summing over charges and each of them is at a different geometric location But I don't know how to get dq and R to talk to each other so I can add this up in a consistent Covenant way. I don't know how to add up dq is when I've got ours floating around So we've got to find a way to relate R and q all right. That's that's a problem. We don't know how to solve yet So let's see if we can attack each of these pieces and By doing so come up with a relationship a geometric relationship between what charge you're looking at and where it is Okay, so let's start with R squared That's usually the easiest piece to deal with it's just going to be the length of a hypotenuse squared Well, I've written my coordinate system. I already told you before you've got a right triangle with a height y a base length x Okay, and a hypotenuse there all right, so if I draw the components of our vector For the piece. I've shown you here. It has a piece that points to the right and a piece that points up and The length of that is just going to be The length of it squared is going to be the x-coordinate squared Plus the y-coordinate squared That's really all I can do at this point. I know that my point p is some height y above the line That's never going to change for this problem I know that this particular Charge is located some distance x away from the origin So I write that down and that's about it. That's about as far as I can go right now Let's write down our vector We need that in order to get our hat. So we might as well do that next So our vector I've already kind of sketched what it's going to look like here It's got a piece that points in the positive I hat direction It's got a piece that points in the positive J hat direction So it's a distance x in I hat plus a distance y in J hat And again, that's about as far as I can go with this right now Okay, finally We have to do our hat and to get our hat. I divide our by its magnitude Well, this is going to look pretty I got x I hat plus y J hat over the square root of x squared plus y squared I feel like we've gotten in a worse position now. We don't really know what's going on here. All right, so let's let's write down what we've got Clean some of the chemistry off the board here last class All right, so let's see. Let's see what we've done. I think we've made the problem worse We've got de vector equals k. Okay, we know what that is dq. No idea what's going on there We got our squared in the denominator So we got x squared plus y squared down here, and then we've got this our hat vector, which is x I hat plus y J hat all over the square root of x squared plus y squared Now we can go one step further and kind of group some things here. We've got we've got an x squared I totally agree Lucy. I've got an x squared plus y squared. It's fine. Trust me That's what's happening inside of me right now as I look at this. Okay, I got an x squared plus y squared here I got a square root of x squared plus y squared here I hope this looks familiar to people, but you can rewrite the square root in a suggestive way You can take x squared plus y squared raise that whole thing to the one half power and that's equivalent to the square root And when you do that you see that now you're multiplying something with a power of one times the same thing with a power of one half And so you can rewrite this as I'm gonna pull this over here De vector equals k dq all over x squared plus y squared to the three halves And if you're not sure what happened there review your fractional review your addition of powers when you multiply things together It's a fun weekend activity for Labor Day Okay, and then you have your your remaining numerator in the in the unit vector x i half plus y j half Now I feel like we've made this problem worse, but we are on the cusp of a breakthrough Okay, because we have one piece. We haven't dealt with dq Is there a way we can relate the little piece of charge occupying a little piece of length Can we relate the charge to the length somehow through a number any ideas? Javon got any thoughts on this Just trying to fly into the radar Yeah, they go linear charge density linear charge density rides in and saves us Because this is a charge per unit length and we know we've got a little bit of charge Occupying a little bit of length So lambda is going to be equal to q over l whatever that is some constant It will also be able to dq over dx that little bitty piece of charge over the teeny tiny piece of length that it occupies That's a constant and So now we see we can relate Charge and geometry Charge is related to geometry position in the problem and that's good Because now we see Something very suggestive happened at the end of this De vector is k and we're going to kind of rewrite these things up a little bit so you kind of see the Calculus of it x i hat plus y j hat dx So I put the dx even though I could have put lambda dx up here like I did here I just moved it and these are just numbers that are multiplied I can move them anywhere in the product and it doesn't matter okay So I just moved the dx off to the right suggestively because you know you may be familiar with with Seeing something like you know dy equals a dx and if I want to get y Y is the integral of dy which is the integral of a dx Okay, so if I want to sum up all the little functions of dx multiplied by a and Get y I just have to put that curly s next to it right and add up So that's what we're about to do Okay, we've got about as far as we can get Setting up this little piece of charge in terms of coordinates Geometry and constants coordinates Geometry and constants once you've gotten it as far as you can go in those directions. It's time to integrate Okay So that's what we're going to do That's as far as you can take that one piece and now it's time to sum them all up all right We've used this Don't worry you're going to get to exercise this. Yeah Oh, I'm just giving that as an example So in you know in a calculus class or in a calculus video or something like this You might see you know something like you know y is some function of x so y equals a times x whatever a is okay, and The differential of y Is a dx and if you want to integrate those Differentials so does anybody know what the inner I mean the this is like the simplest integral to do You're just taking the sum of all the little pieces of y and then it better return the length y when you're done Okay, that's the nicest integral you ever have to do in life That is equal to the integral of a dx whatever that is okay, and that might be tough or it might be easy if A is a constant. It's easy if a depends on x It's not and you probably have to go look up the integral or put it into Wolfram alpha Which is an a web front-end to Mathematica something like that okay? I Don't care how you get the integral once you get to this point Your bike three seconds away from solving the problem because you just have to integrate Okay, and how you do that I leave up to you you can do it yourself. You can look it up in a book Books are a thing anymore. You can use the internet use some program. You purchase to say what you did okay? So to get the total electric field E. I Need to integrate all the little pieces de and that means I need to integrate k lambda over x squared plus y squared to the three halves X i hat plus y j hat dx So all I did to get to this step was put the integral sign in front of it and say whatever that is It's equal to the total electric field That's just the definition of a sum the sum of the parts equals the total Okay, so there's the total. I want that I have that so I need to do something with that Now let me ask a question if I gave you the following a Let's see a x DX, let's do it this way a x plus b x squared so there's some function of x DX and I told you to integrate that What might be the first thing you would do to make your life simple? Yeah, you can take out the axe That will make your life simple because now you'll have x multiplying another function of x awful Because then you'll have to integrate by parts and yeah, don't do that All right, so you've just made your life more difficult You're one to watch. Yeah, okay, no problem What are you gonna you can't but I want you to integrate it distribute the DX distribute the DX Okay, yeah, the DX is just a little you know It's a little infinitesimal number and like anything an algebra it can be distributed So we can rewrite this as the integral of a x DX plus b x squared DX and that just breaks into two integrals a x DX plus the integral of DX squared DX you can distribute So there's really two integrals added together up in that funky looking thing on the right-hand side of the electric field Okay, you've got an integral of x over x squared plus y squared to the three halves And you've got an integral of y over x squared plus y squared to the three halves both DX Okay, so I'm gonna go ahead and write that Just gonna do the same thing I wrote there in simple form like this nasty thing up here Okay, so E Equals all right. Well K is a constant Land is a constant. I'm tired of having my constants inside the integration They're not going to participate in the integral. So I'm just gonna yank them out in front and I've got the integral of X over x squared plus y squared to the three halves I had DX plus the integral of y Over x squared plus y squared to the three halves J hat DX now This is just a unit vector. It's just a constant thing that points.  I mean, I think you guys can all do this Okay, but if you want to sort of set back and go where where do I have to put the most brain power into a problem? It's setting it up. It's getting that that thing to integrate in the first place after that It's just executing the rules of algebra and calculus Okay, which gets wrote after a while the physics of it is going from the picture with charges To something mathematical that you can sum up later So you have to use physics to get the thing you can add up and then you just do math All right, so because I would like you guys to play around with your own problem We're gonna do this like a baking show and then a miracle occurs and the cake comes out of the oven, okay? Before I show you what's gonna happen in one of these integrals. Let's step back and look at this picture again Let's imagine that this is a positive charge that's distributed on this line Okay, so all the little itty-bitty pieces are also positive and let's say I pick a piece over here and I pick a piece in equal distance from the point P over here and they have the same magnitude. There's both dq They're both positive The electric field from this one points where Does it point toward the point P or away from the point P? It's a positive charge Towards point P because positive charges are the source of electric field So this electric field emanating out in all directions, but if we're just at point P There's a line that connects the electric field to that point P All right now what about from the symmetric mirror twin of that charge over here equidistant from the origin But over on the right hand side, where is its electric field point? Away from point P so like that Towards yeah, because it's also a source of electric field Okay, so the line of the electric field is converging on point P. They are Equal in length Okay, which are their components points in opposite directions horizontal or vertical? Horizontal yeah, the horizontal components are doing this the vertical components are adding up or canceling out We'll do this again adding up Okay, now you're doing the electric field things Nothing guys it's Thursday. We're in like the second week of classes more energy, please I've got 13 weeks left in me. What have you got okay? Every semester all right think about that for a second.  You just do the same thing for 15 weeks every semester Thank you. Thank you for giving me some small symbols of joy in my life Okay, all right. So yeah, so the horizontal components cancel out the vertical components add up So what do we expect that integral over that thing in the x direction to equal? Zero yeah, well you're not going to commit you're not going to let everyone in the back row here you Sophie said zero So just in case we're wondering okay Yeah, so for every piece that's over here on the left There's a twin piece on the right whose x component points in the opposite direction, but it's equal magnitude and so Without doing any math. All right. You just look at this problem goes there is a symmetry There's an infinite line to the left. There's an infinite line to the right So there's always going to be a twin charge over on the left for one on the right that cancels out in x component I expect that integral to be zero and in fact if you plug it into Wolfram Alpha or whatever you want to do You will find out that that integral is in fact if you do it. Let's put some limits in here symmetrically From negative infinity to positive infinity You'll find out that that is a big fat nothing zero No x component in the resulting total field. Yay Now you just have to do this one This one non-zero because all the white components all point in the same direction and add up Okay, now they have different strengths as you go further and further and further away but they all add up and The result of doing this one If you work it all the way through you will find that the total electric field is 2k Lambda over y in the j hat direction Okay, so Y is not something that varies in the integral But of course you're now free to say well, I'm going to move the point P twice as far away Okay, so now we find me let's say I started out at y equals one meter and I move the point to y equals two meters What happens to the strength of the electric field from this line? Does it double does it have does it go down by a four? double the distance What happens to the strength? Fourth of it is there a squared somewhere that I didn't notice to double see doubling it would if you square it would go down by four It doesn't linear so you double it and goes down by two Okay, so it's kind of cool about this is while each individual charge each little point in this thing The force declines as a function of one over r squared when you add them all up They kind of reinforce each other and so in fact the electric field of the total only declines as Linear falls that you go twice the distance that goes down by half you go four times the distance that goes down by four Okay, not 16 All right, so that's just one of these effects when you get a bunch of charges together You have to be a little careful watch your intuition read the equation make sure it says what you think it says, okay? If we had a positive charge density Then the electric field would point in the positive y direction We kind of saw that already when I was doing the dance right if we have a negative charge density some negative q per unit length Then the whole thing flips okay, and you're in the negative j hat direction So lambda can carry an additional sign if it's a negative charge density that would flip it around, okay? So what you wind up having here And I don't think I have a sketch of this But I have it in the notes as if you kind of imagine here's the line and you go anywhere around it a distance Why the electric field for a positive charge density will always radiate outward and it will fall off linearly with distance So this cord if it's carrying a net charge Carries an electric field with it that radiates out uniformly in all directions around the long axis Okay, and it declines linearly And so something to keep in mind is that all devices around you right that carry a net electric charge through them a current They have electric fields that they're emanating and so, you know You have to keep that in mind when you're designing equipment if you're gonna put a patient In an instrument that you know measures something about their electric currents or whatnot You have to keep be mindful of the fact that you can disturb their own currents by using electric fields from your own equipment So things to keep in mind even in medicine You have to be a little bit careful if you're using a new instrument hasn't been properly shielded against its own fields for instance, okay? All right, so here's the problem. I want you guys to do for the rest of the class It's a small variation on what we just did here. All right, so much of this will apply But I want you to try to step through it on your own Now the line is not infinite. It's finite and it's all to the left of the point P So imagine the copper wire is now a length L, but it's only to the left of the point P Okay, it carries again a charge q distributed uniformly over the length L Get the electric field for this at the point P Alright, so your goal your goal is to set up Something starting from this point charge Coulomb's law And you're going to try to get all these pieces written in terms of coordinates and constants and geometry Coordinates constants and geometry can't repeat that enough. That's what I'm looking for right? So you're going to set up this differential Which can then later be integrated like we did here. Okay, so we're together in groups I want you to partner up with two or three, you know people together Work together. Okay, and if you don't like the person you're sitting next to then quietly You say I gotta go to the bathroom and then to shuffle to another row. All right All right All right, and I expect you you're talking. I want you helping each other. Okay, if you have questions Come talk to me and if you need to build your chops in calculus Don't be afraid to meet with me outside of class. We can we can work through that together. Okay?


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