No, it's not, no, it's not, no, it's not, no, it's not, no, it's not, no, it's not, yes, it is, yes, it is, yes, it is, yes, it is, where was the evidence for God that was the that was the entire first part was is there evidence of God and I didn't hear not only any objectively verifiable empirical evidence for God, I didn't even hear any intuitive evidence for God, just a lot about the value of intuition and how evidently as an atheist, I'm all about military power, which I generally despise despite having done eight years in the military. And that's not consistent with my secular humanism, and nothing that I could view as evidence of God. No, the whole point was to question your standards. That's your subject of debate. Hey, I didn't interrupt you when you Correct. Called what I said a diatribe. Let's try to be civil here. I am trying to be civil. Then don't interrupt me. Then don't interrupt. Interruption is. Don't interrupt me. Uncivil. Okay. So as I was saying, the whole point of this opening is to question your standards of evidence. If you want to say that, well, there's no scientific evidence. When we do experiments and open the microscope and look at in the beaker, we don't see God. Then I can concede that. So what's the point of that point that your opening was about? My opening was to take the discussion to a higher level of what are our standards? What is our epistemology? You're assuming a atheistic epistemology that I don't accept. And the most most people in history and even today don't accept that. So that's, that's point number one, as opposed to as for evidence of intuitions that people believe in God. We'll talk about it in the next part of the debate, but there's this is something that's established. There's a natural theology that is established within the cognitive science of religion that people have intuitions about spirit beings. They have intuitions about a purpose to creation. They have intuitions about there being an afterlife. These are all things that are established within the cognitive science of religion. Is that a pause for me? Yes. Cool. So I wanted to do a debate on Islam versus secular humanism and which one's better for the world. But Dandel didn't want that. And then James kept coming back to me with potential topics for a debate. And I pointed out various problems with them and everything else. And then finally I gave up and just the three different topics that he wanted over three hours is what I agreed to. And so I'm given a list of topics and topic one is, is there evidence of God? I rest my case because he just said that the entire purpose of his opening was to question my epistemology. I am irrelevant and my epistemology is irrelevant to whether or not there is evidence of God. And if you demand that the first hour beyond is there evidence for God and you do not address that topic and admit that instead you've decided to go with a different topic, you have defaulted and I rest my case. No, it's the same exact topic. If you have a debate topic. Part of the debate is to analyze the topic and the assumptions that go into one position or another. I'm analyzing the assumptions that go into the first sentence or the second sentence that you had was that this kind of scientific analysis is the best route to truth. I am objecting to that and proposing an alternative. How about you explain to us and justify why it's the best route to truth? Because the subject of the debate is, is there evidence of God? Yeah, how do we determine that? You're asserting that it has to be scientific evidence. The subject of the debate is, is there evidence for God? My answer is no. And I talked about what sort of evidence I would accept or not accept. I didn't say anything at all about shutting down intuition. I didn't say that intuition should be sidelined or less important or that it has no. I thought we were done interrupted. Or that it has no importance. I didn't do any of the things that he asserted. And not only did he not present any evidence of God for us to address, but he fully acknowledged that that was not the purpose of his opening statement. I rest my case. So where's the evidence that the external world exists? That's not the subject of the debate either. You, I want to know like your standards of evidence for God. Do they have any meaning outside of that particular question in the very specific way that you've defined it to, to set the debate up in your favor? Is there anything else that is scientifically verifiable, like the external world? Yes. Like the principle of non-contradiction, please give me the evidence, the objective, objectively verifiable evidence that the law of non-contradiction is true. I'm not the subject of this debate either. And after being accused of setting this up so that it would be easy for me to win, after acknowledging, he chose these topics that I did not want to address. And now it turns out that he also does not want to address. I don't know what to do. James? No, no, there's plenty of evidence. There's plenty of evidence. If you ask people, start for evidence, if you ask people for evidence of God, they will point to their sense that God exists. They will point to their sense that when they look at the world, they see it as being created by a supreme being for a purpose. When you ask people about any number of things that are not scientific, they will have a tendency to answer in specific ways. These are studied within the cognitive science of religion and psychology generally. If you ask people for evidence of the external world or basic arithmetic propositions, there's a tendency to answer in consistent ways in a universal fashion. What this tells us is that the human mind has a certain structure. It works in a certain way. And we have to understand the human mind in order to ask questions about morality, religion, aesthetics, logic, mathematics, all of these science, right? Empirical data, all of these things have to be understood with reference to human psychology. So it's not irrelevant to the debate. It's actually a core first step of being able to debate evidence for anything, let alone evidence for God. So what we just heard was that if you ask people, they'll tell you that they believe in a God. Some of them even say they intuit it. I'm still asking and still waiting for a demonstration of evidence for God. That's evidence that people believe in God. And if you just said, hey, I want to debate whether or not people believe in God, I'd say, why would we do that? I clearly agree that people believe in God. I used to believe in God, but I didn't do it necessarily because of intuition. Although some people might do it for intuitional reasons. Some people might think that they're doing it for good evidence reasons. But when I found out that I didn't have good evidence and when I found out that intuitions could be wrong. And if you're going to have intuitions about, oh, I don't know whether or not the restaurant's going to be busy. That's probably based on past experience and data that you're just using your gut to assess. And so what you're describing as potentially intuition there isn't actually intuition, but it's based on data. But we don't have any data that I'm aware of for God. We don't have any evidence that I'm aware of for God. You haven't presented any and that's the subject to the first hours of debate. Intuitions are evidence. Intuitions are evidence just because you don't accept them. That doesn't mean that they're not evidence. There are different types of intuitions. I didn't say all intuitions are equally compelling. There are some intuitions that are so compelling that no one has questioned them for most of human history. Like the intuition that there is an external world, for example, or the intuition regarding the law of non-contradiction. Certain moral intuitions like it is wrong to harm people. People have universally had this intuition. Why? Because every moral system, every religion that we see has this principle in it implicitly or explicitly that it is wrong to harm people without reason. That is evidence of its truth in so far as the human mind is capable of accessing the truth. That's the point. And the belief in God is also one of these very strong intuitions that human beings have that they developed from childhood. So that is evidence. You don't accept it as evidence. That's my point. Boy, have I got some surprises for you. Daniel seems to think that nobody's questioned reality. I don't evidently have never heard of solipsism. For most of history, are you interrupting me again? What's good for the goose? Solipsism in the study of this within philosophy is something that is robustly argued all over. It's almost argued more than whether or not atheists can be rocks or whether or not tacos or sandwiches. Solipsism is the issue of can we trust and do we know that the outside world that we think is the outside world that we experience? Is it the real true world? And as far as I'm aware, there is no solution to the problem of hard solipsism. But when you say that people's intuitions about God count as evidence, as I was pointing out, whether you're going to have objectively verifiable facts or objectively verifiable empirical evidence or not, at a minimum, the evidence that you demonstrate someone's intuition, if you want to claim that's evidence, you have to make a demonstration to show how that intuition is consistent with a specific God concept and excludes other God concepts and how we can demonstrate that it is probably correct. And you haven't done any of that. You've just asserted that people have intuitions about God and that we shouldn't dismiss them. I didn't say we should. You've asserted from the beginning in your opening statement that the route. I think you use the word route to understanding reality and truth is through this kind of scientific analytic investigation. What do you want you asserted that you asserted that so why can't you just justify that? Why can't you tell us why we should accept that standard? Because the first hour of this debate is not is Matt's epistemology sound is is there. Yes, it is. No, it's not. No, it's not. No, it's not. No, it's not. No, it's not. No, it's not. Yes, it is. Yes, it is. Yes, it is. Meanwhile, what I said is that scientific inquiry is the most consistently reliable pathway to demonstrably understanding reality. I didn't say that intuition couldn't get you to the right answer. Intuitions need to be demonstrated in their reliability because the wise person is human teaches proportions their confidence to the evidence. You can have intuitions and they might be right, but the way to be confident and the way for them to count as good evidence is to show that they are probably right. So asserting that people have intuitions doesn't make them evidence. It doesn't make them reliable. And it doesn't mean that people's intuitions about whether the God is a Christian God, a Scientologist God, a Hindu God, a Muslim God, or some other God that nobody's proposed as any demonstration that it's likely to be correct. And this hour of the debate is supposed to be about evidence of God. I still am waiting. So your standard of evidence takes out all moral claims. Moral truths, I'll say, actually, because I do believe it is a moral truth that harming others for no reason is wrong. I can't demonstrate that. I can't bring you peer reviewed studies to establish that. I do believe that the law of non-contradiction is true. I can't bring you scientific evidence for that. I can't bring you. I can't demonstrate that in a proof. I do believe that the external world exists. I cannot demonstrate that through a proof. I can't bring you scientific evidence for that.  That is a truth and I will stand by that. But there's no scientific result that will say that that is true, but it is true. That is reality. We all have these universal truths that we abide by an understanding reality, but none of that has to do with scientific evidence. None of that has to do with having this kind of deductive proof, yet it's still true, yet it's still reality. What the atheist does, and in general, not just Matt, the atheist says that none of that is really real. And we don't need to talk about that. Let's just talk about what is scientific. But this is a drastic, violent limitation on reality that the vast majority of humanity, not only today, but throughout history, doesn't share. People don't have this scientific reductionist view of reality. So if you go back to the beginning of my opening statement, not the Mitch McConnell joke, which was really good, by the way. But if you go back to the beginning where I was describing things in addition to talking about the nature of evidence and everything else, I think I specifically pointed out that there are things where we're not going to be able to point to empirical evidence. And I think I used morality as an example for that, to suggest that I am tossing those things out is not remotely accurate. And I guess he just missed part of my opening. But my opening was about evidence of God, not about competing epistemologies, so I'm still waiting. Well, the difference is when it comes to morality, I'll stand up and say, this is true. And it's not something that I can doubt. If I doubt it, I doubt my reality. But your position, and you can correct me if I'm wrong, is that morality is something that we can't have objectively verifiable facts about. Our positions are not the same on morality. My position is shared by the vast majority of human beings and no one even questions that's people's reality. I doubt reality. I doubt many things that I intuitively feel about reality. And yes, our view on morality is very different with something I'm sure we'll get to in a little while, which everybody's already aware of. When it comes to moral truths or let's say the law of non-contradiction, identity, non-contradiction, excluded middle, the foundations of logical thinking are presuppositions. We can't demonstrate that they're true because you'd have to assume that they're true to try to prove they're false, which means they're not falsifiable. However, what we can do is demonstrate that they consistently seem to be inviolate. That means that there doesn't seem to be anything that breaks those rules, but we don't have an exhaustive understanding of the universe. And so beginning as a practical necessary assumption to say I would like to reason, these are the foundations of reason that I'm going to begin with, identity, non-contradiction, excluded middle, and they continually consistently demonstrate to be true and reliable and have never been shown to not be. It is a reasonable intuition or inference or presupposition that we should continue to use them until such time as somebody demonstrates, hey, we found a problem with identity, non-contradiction, excluded middle. And now you have to rethink whether or not you can use them as a foundation, but until then it's like, you know what, I rolled a dice and I rolled it over and over again and I calculated the probabilities and this dice consistently conforms to the probabilities, but it might be the case that angels are ticking the number that shows up on the dice every single time and they're just doing it consistent with the probabilities that I understand. And any day now that angel could just turn it to something else. So I better not, I don't have any foundation for probability. We have loads of foundation for probabilities. We have loads of reason to think that something is true. What we don't have a way to demonstrate is that it's impossible for it to be otherwise. Yeah, so how would you falsify the principle of non-contradiction? I just asserted, I just literally said you cannot falsify non-contradiction. So it's not up to be falsifiable. So why do you say it seems to work as if there's going to be a future point where it's not going to work and therefore it will be falsified? Am I speaking English? I said these things are unfalsifiable. They are presuppositions that continually demonstrate that they are true. There's no reason to think that they could be violated in the future, but you can't demonstrate that. And so it is a presupposition. I am as convinced as I can be of anything that the foundations of logic are reasonable, but you can't prove it. This is the foundational problem of logic. Why do you accept it? Oh my gosh. If I pick up a pen and I try and write with it and it writes every time I pick it up and write with it, then I'm going to view that pen is reliable right up until it stops being reliable. That's the same thing for identity non-contradiction excluded middle. Those things have continued to demonstrate that they seem to be. It's not an empirical thing. It's not an empirical thing. How can you demonstrate something that's non-empirical? How can you demonstrate that harming someone is wrong? Is there going to be a future point where we discover, oh actually harming people for no reason is not wrong. It's actually good. It's not an empirical thing. Like you're making a category mistake. Like these are non-empirical things, but you're applying this empirical standard of falsifiability to everything. This is just a basic category mistake. So everybody pay attention to what's happening. This grandstanding is ludicrous. Are you speaking English? I'm sorry. People understand me. Rewind it. I literally have to say the same thing. You don't get grandstand. Just answer the question. Your principle of falsifiability. You don't get to determine. You don't get to decide what question I answer and what question I don't answer. What's actually happening here right now.  What's happening right now. Yes, you are. You're hurting my feelings. I know. You're breaking my heart. Wait till we get to the other problems. So what's happening here is I explained it and then I explained it again. And when he didn't have an answer, he instead tried to shift the topic to is harming people wrong? Are we going to find out that someday harming people is not wrong? And then he shifted that topic to is harming people for no reason wrong? When that's not the subject of this debate. It is not the subject of this hour debate. And it is not what we were talking about. Are you going to be able to stay on topic and eventually present some evidence of God? Or are you going to keep grandstanding and deflecting and pulling up topics that we weren't talking about? So if you apply the standard of falsifiability, that's exactly what's in question. That's what the whole opening was about questioning that standard of scientific evidence is the arbiter of truth. You haven't addressed that at all. You just grandstand to the audience and then you keep saying that. Well, we don't have evidence for God. Yes, I know that's the question. That is the debate topic, but we're trying to analyze what does evidence actually mean? What are standards of evidence that are required? I say that intuitions that human beings have universally from childhood are evidence. For God, insofar as we can understand truth, insofar as we can understand reality, that is evidence. You don't accept that as evidence. And you say that, well, this is not objectively verifiable. And I ask you, why is it not objectively verifiable? You say, well, this is not something that's empirical or scientific. Why would we ever accept this? And then I say, well, what about all these other things that you accept that you seemingly accept? But they don't have that standard of proof, yet you accept them. Do you accept that there's an external world? Do you accept that harming someone for no reason is wrong? Do you accept that even though you don't have any empirical proof? So why won't you accept that God exists? So I was just accused of saying, why would we accept it if it's not empirical? When I just finished explaining that identity, non-contradiction, excluded middle are not only not falsifiable, but are an example of the thing I highlighted at the beginning of my opening about things that are not based on empirical evidence. I didn't address the question at all about whether or not I think there's an objective world that we're experiencing. So Daniel is arguing against a fictional strawman of me and still presenting no evidence of God. You accept law of non-contradiction? Yes. Why? Where's the empirical evidence? Where's the empirical evidence? As I've explained now four times. That's something that's not empirical. That's my point. Correct. Correct. So then there can't be any empirical evidence for it. Yet you accepted it. I didn't say there couldn't be any empirical evidence for it, but that's not why I accepted it. What could be? Are you going to let me answer or are you going to talk over me again? I explained why I accepted it because it continually demonstrates its reliability. And I also pointed out that I accepted it initially as a free supposition because there is no way to demonstrate identity, non-contradiction, excluded middle are always true, but there is a way to show that they are true in every example that we can come up with. You can do this with a simple Venn diagram to show that A, not A, and everything is either A or not A, and nothing is both A and not A. This is what a single Venn diagram with a single circle demonstrates. I'll come up with an example that suggests or shows that identity, non-contradiction, or excluded middle aren't true. I'll come up with an example where they're not true, and I'll stop believing them. Kind of. I'll stop believing that they are going to continue to be reliable because now you'll have demonstrated that there's a circumstance where they're not reliable. But much like the pen, until there's a demonstration that this is going to not be reliable at some point, which for pens we know. And until that time I'm justified in continuing to use logic as a presupposition that continues to demonstrate its viability and its reliability. I said nothing at all about why should we believe something if it's not empirical. I did not say at any point that science is the only way to knowledge understanding. What I said is the most consistently reliable, demonstrable pathway to an accurate model of reality. If you're not going to address what I actually said, could you finally present some evidence of God?


Everybody now here for late in sports cards ripping one box of 2023 tops finest baseball. This is for Jose M. Good luck Jose Thanks, all everybody for hanging out grab boxes chatting Hitting the like button following subscribing It is much appreciated Pretty fun Sunday here of a personal we have Sunday funding group race with four starting at five On the main channel more personal with Kyle on the late in two channels starting at five Grab your spots in your boxes. This is the last break of the day. I'll jump off here pretty quickly after I'm done with this box Cal Mitchell and Aranda JT real Muto purple Trout and judge Shea Lange leaders rookie refractor rookie design variation Nolan Gorman And Josh young rookie blue refractor auto to 150. There you go. Jose Grats on the young little magnet for you and tow bar You don't really tie the day together as a super right here in this last box There's Adley our in auto headliners Tony. There's Garrett Mitchell rookie refractor Jnami Christopher Morel rookie Kyle Tucker and McClanahan Leave her tour and Kodai Senga. That is rookie design variation refractor to 99 ice card It's Cabrera onion Sosa rookie refractor Cunha and Alvarez Albert Pujols headliners and Bubba Thompson rookie auto Rangers rookie box here Zuki Jordan Walker rookie Cal Raleigh blue to 150 Bo Nailer Spantino Logan Ohapi rookie Shohio Tani refractor Moreno and Senga Last pack Yoshida headliners Ichiro Machado and confordo that'll do it for your box Jose. Grats on that Josh young appreciate it We'll get these right out to you


In our last lecture, we had described the concept of electric field and magnetic field transformation. We had said that in relativity, a field can be mixture of the two. What it means that if in a particular frame, the field experienced by a charge is purely electrical, it is likely or in general, it will always be that in any other frame, it will experience both a combination of electric and magnetic field.  It depends on the frame from which you are viewing. So, this is what I am recapitulating. We discussed the transformation of electric and magnetic fields. Using this transformation, we found out that if I know the field, electric and magnetic field in a given frame, how do I find out the electric and magnetic field in a different frame? This is what we had discussed in our last lecture. Today, what I will try to do is first to tell that some of these equations can be derived in a different fashion, because they happen to be somewhat interdependent. So, that is the first aspect that I will discuss. Then I will give one example, one specific example of how electric field and magnetic fields will transform once I go from one frame to another. So, this is the electric field transformation that we had written. If I know in a frame S, the electric field components, it means I know E x, E y and E z. And I know the magnetic field components that is B x, B y and B z. Then, in a different frame S, of course, S and S frames have to have the same relationship as we have discussed in the earlier Lorentz transformation. This E x will turn out to be equal to E x, E y will turn out to be equal to gamma E y minus V B z. And E z will turn out to be gamma E z plus V B y. Similarly, we can write the inverse transformation, which means that if I know the fields in the primed frame of reference, I can find out what is what are going to be the electric fields in unprimed frame of reference or in S frame of reference. Now, these equations tell only half the story, because they only tell you how to evaluate the x, y and z component of electric fields. We also require equations which can tell us what will be the x, y and z component of the magnetic field. So, there is a different set of equations which gives the transformation or which enables us to find out the magnetic field in a frame if I know the electric field and magnetic field in a different frame. So, these are the set of equations. So, B x prime turns out to be equal to B x, B y prime turns out to be equal to gamma B y plus V by c square E z, B z prime turns out to be equal to gamma B z minus V by c square E y. Similarly, this inverse transformation, the fields are known in S frame of reference and using these equations, I can find out what will be the magnetic field in the unprimed frame of reference or in the S frame of reference. So, these are the equations which enable us to find out the magnetic field. So, this in combination with the earlier three equations, which are about electric fields, I can find out all the components, the electric field components as well as the magnetic field components in a given frame. Now, what I wanted to tell is that these last two equations which we have obtained here, for example, can also be derived using the last two of electric field equations, which are these equations. So, let me first discuss these particular aspects because there is some sort of interdependence of these equations on each other. So, let me first discuss that particular aspect before we come to an actual example. So, this is what I have written. Before we proceed ahead, you would like to demonstrate that the transformation of y and z component of magnetic fields can also be obtained from direct and inverse transformation of electric fields. So, this is what we will try to initially try to show. So, what I will do? I will first write the second equation as I said from both the sets. Here on this particular piece of paper, I have already written these equations. These are the equations which enable us to determine the electric field in a particular frame of reference. So, let me look at the second equation. This is this equation as well as this equation. This equation tells me that if I know E y and V z, I can find out E y prime. This equation tells me that if I know E y prime and V z prime, I can find out E y. So, what I will do? I will try to eliminate E y prime from this particular equation using this equation and as you will be able to see that from this we can obtain what will be the value of B z prime or the magnetic field transformation equation. Similarly, if I use these two equations and eliminate E z prime, I can find out a transformation which gives me the value of B y prime if I know the electric and magnetic fields. So, let me first attempt that. So, these two equations as I have said are the second equations which I had just now described. So, E y prime is equal to gamma E y minus V B z and E y is equal to gamma E y prime E y prime plus V B z prime. This E y in this particular equation, I will substitute this value of E y prime. So, here in place of this E y prime, I put E y prime is equal to gamma E y minus V B z. So, this is what I have put it here. This is this particular quantity which is here is replacing this E y prime. The second term term is as it is V B z prime. Now, what I will do? I will expand it. I will multiply here. So, once I multiply E y and V B z by this gamma, it has to be further multiplied by gamma, it will become gamma square. So, let us look at this particular equation. This is the equation which I have just now written on my last transparency. So, as I said, when I open it, when I expand this particular bracket, there is a gamma here. There is another gamma here. So, this will become gamma square. This will become gamma square E y. Similarly, there is a gamma here. There is a gamma here. There is a negative sign here. So, it will become minus gamma square V B z plus this term remains as it is except that this gets multiplied by gamma, which is here. So, it becomes gamma V B z prime. Now, what I am trying to do is to find out the value of V z prime. So, I want to take this on the right hand side. If I take, want to take this particular thing on the right hand side, I will get the equation which is this will become negative. So, this becomes let me first look at this. If I take this on the left hand side, I am sorry and E y on the right hand side, then this V z prime I have to divide by gamma. Let me write this particular thing to be more clear. The equation which I had was E y is equal to gamma square E y minus gamma square V B z plus gamma V B z prime. So, I take this on the left hand side or you can put I take these things on these two things on the left hand side because this I want to retain as positive quantity. So, I can write this as gamma V V z prime is equal to E y minus gamma square E y. When this goes to this side, this will become plus gamma square V B z. I divide the equation by gamma V. If I divide the equation by gamma V, I will get B z prime is equal to E y by gamma V minus gamma square E y divided by gamma V plus gamma square V B z divided by gamma V. This is the equation which I have written here. Sorry, this involved a few steps. So, B z prime is equal to E y divided by gamma V minus gamma square E y divided by gamma V plus gamma square V B z divided by gamma V. Same equation which we just now wrote on this particular piece of paper. Now, this gamma square, there is a gamma square here, there is a gamma here. So, this will cancel with one of the square and this becomes just gamma. Similarly, there is a gamma here, there is a gamma square. So, this will become gamma. Here, this V and this V will cancel out. So, this particular term, the third term just becomes gamma B z. Here, you have just gamma E y by V and this term remains as it is E y by gamma V, a simple algebra. Put this equation here. From these two, I take E y common. So, I write E y. What is remaining in the bracket is 1 divided by gamma V minus gamma by V. This term is gamma B z as it is. Now, what I do? Out of this particular equation, I multiply it further by gamma. So, this equation becomes gamma E y by V. If I multiply by gamma, these things have to be divided by gamma. So, I divide by gamma. When I divide this term by gamma, I get 1 upon gamma square. When I divide this term by gamma, I just get 1. This V has been taken out here. So, this equation becomes gamma E y by V. V comes from these two equations and 1 minus 1 divided by gamma square minus 1 plus gamma B z. Now, this equation can be simplified because I know what is the value of gamma square and therefore, I can always find out what will be the value of 1 upon gamma square, which I am doing in the next transparency. As we know, gamma square will be equal to 1 upon 1 minus V square by C square. So, if I take inverse of gamma square, when this we have used number of times earlier also, it becomes 1 minus V square by C square. So, here it becomes 1 minus V square by C square. This one will cancel with this one and what will be remaining is just minus V square by C square. So, this term remains here and this whole bracket gives me minus V square by C square. So, this is minus V square by C square plus gamma B z. This gamma can be taken out. I get B z minus V by C square E y, which as you would have realized that this is the transformation equation which gives me the value of B z prime, the z component of the magnetic field. If I know the z component of magnetic field in S frame and the y component of the electric field in S frame of reference. Similarly, you could have taken the third set of equations as I have described just now and eliminate E z prime from that particular equation and then I could have obtained transformation equation corresponding to the y component of the magnetic field. In that case, B y prime will turn out to be equal to gamma B y plus V by C square E z. So, as we have seen that the last two equations of magnetic fields transformation can also be obtained just by using only the electric field transformation and just manipulating the last set of equations. Of course, you have to use the direct transformation as well as inverse transformation and you can manipulate these equations to get this result. I would just like to mention one more point because many times, I mean of course it is always we have always been telling when we started special theory of relativity that the initial conditions that we have put on S and S prime, the relative velocity was always along the x direction. But sometimes, we will prefer to write a little more generic equation which does not have this relative velocity between the frames only along the x direction. And if you want to do that, these equations of electric field and magnetic transformation can also be write it along the longitudinal and the transverse direction. That is the direction parallel to the relative velocity motion direction and perpendicular to the relative velocity motion direction. So, this is what I have written in case we do not want the relative velocity direction between the frames along x direction, we can write the perpendicular and parallel to the relative velocity components. So, when I say perpendicular, it will mean perpendicular to the relative velocity between the frames and parallel which means parallel to the relative velocity between the frame. The results somewhat obvious, but nevertheless let me just give because this sometimes we give these set of equations. In such a case, the transformation equations for the electric field can be written as. So, many times you will see in the text book they write this type of equations that E parallel prime is equal to E parallel, E perpendicular prime is equal to gamma E perpendicular plus V cross B, the perpendicular component of this cross product. So, essentially the other two equations which we have written y and z component can be merged into this particular way of writing these equations. So, basically you will have to remember in that case only the two equations. Of course, the first equation is obvious because along the direction of the relative motion the fields do not change. It is true for electric field as well as the magnetic field because even for magnetic fields we got Vx is equal to Vx prime. It is only along the perpendicular to the relative velocity motion direction that the fields transform. So, this is what we call as a perpendicular or transverse transformation of the fields. Similarly, we can write the equation corresponding to the magnetic field also. So, for magnetic field I will write V parallel prime is equal to V parallel and V perpendicular prime is equal to gamma V perpendicular minus 1 upon c square. For this here there is a term of 1 upon c square V cross E perpendicular component of this particular thing. And if you have any worry you can always take V along the x direction and expand the cross product you will get the same three equations that we have derived earlier. So, what I have written this can be verified by taking the velocity along x direction and expanding the cross product. So, this was about the electric field and magnetic field transformation. Let me now take one example, one simple example extremely simple example just to give you some idea of how the fields transform. So, we consider three different frames of reference S, S prime and S double prime. We of course assume that their y and y prime and y double prime axes are parallel in all those things which we have always assumed for deriving the original Lorentz transformation. Now, the speed of S prime and S double prime in S frame is 0.6 c and 0.8 c respectively in plus x direction. So, what has been given are the velocities of S prime and S double prime in S frame. The speed of S prime and S double prime in S frame is 0.6 c and 0.8 c. So, we have three frames let us say this is S frame we have S prime frame and we have S double prime frame. Now, the speed of S prime in S frame has been given as 0.6 c. So, S prime in S frame appears to be moving with a speed of 0.6 c of course, along the plus x direction. Similarly, S double prime is speed has also been given only in S frame which happens to be 0.8 c. So, the speed between these two frames is 0.8 c. So, both the speeds have been given in S frame. Let us go ahead with the question. In the frame S prime magnetic field is 0. So, what has been told that in S frame the magnetic field is 0. While there is an electric field along the y prime direction, put the direction of y prime is same as the direction of y because that is the way our transformation equations have always been written. And its magnitude is E 0 prime or E naught prime. So, this is the magnitude of the electric field which is happening which is only in the plus y direction. So, a person in the frame S says that there is no magnetic field. There is only an electric field which is pointing out in plus y prime direction and it has a magnitude of E naught prime. Now, what I have to do is to find the field in S frame, find the field in S double prime frame and we have to also find out the forces between all these three frames S frame, S prime frame and S double prime frame and see verify ourselves that the forces actually obey the force transformation equation the way we have written it earlier. Of course, this is obvious because these equations we have been derived by using the force transformation. So, this has to be valid, but the idea is to take a simple example and convince ourselves because nothing like working at our own self and try to convince ourselves that whatever I am getting is consistent as I would have expected. So, this is what I am trying to do in this particular example. So, as far as the field information is concerned, it has been given in S frame of reference. We have been told that the magnetic field is 0. It essentially means that B x prime is equal to 0, B y prime is equal to 0 and B z prime is equal to 0. We have also been told that electric field is only in the plus y direction. It means there is no component of electric field in x direction and z direction. Therefore, E x prime is equal to 0 and E y prime is equal to E naught prime which has been given. It is a constant field which has been given as E naught prime. Of course, we have not mentioned about constant, but does not matter. And E z prime is equal to 0. The only field component which is existing in S frame is E prime is equal to E naught prime. All other components are 0. Now, we have said that S moves in S with speed 0.6 c. Hence, to get the fields in S, we have to apply inverse transformation with relative speed v is equal to 0.6 c. Let me just look back at this particular field which I have written earlier in this particular piece of paper. Here, we have written in this particular piece of paper that if you look at this particular frame, S and S frame of reference, S moves with a relative velocity of 0.6 c in frame S. Therefore, if any information which is given in S has to be transformed to S prime, we will use the direct transformation. If the information has been given in S prime and I want that information, equivalent information in S, then I have to use the inverse transformation. Now, here the fields have been given in S frame of reference. Therefore, I must use the inverse transformation to find out the field in S frame. The relative speed is 0.6 c in S frame. So, I still use v is equal to plus 0.6 c, but use an inverse transformation because the fields have been given in S frame of reference. So, if you remember the original Lorentz transformation, the way we have derived, this comes from that, that if things are given in S frame of reference in S frame, if I have to find out, I have to use the inverse transformation. So, this is what I will do. The component of the electric field in S, of course, you know, we have done number of times that for 0.6 c, the gamma will turn out to be equal to 1.25. So, I do not want to derive it again. Gamma is equal to 1 upon under root 1 minus p square by c square. You can, if you do not remember, you can always work it out that if I take v is equal to 0.6 c, gamma turns out to be equal to 1.25. Now, I have to just use the inverse transformation equations which I had written it earlier here. On the right hand side on this particular piece of paper are the inverse transformation equations. E x is equal to E x prime. This is what I have written. E x is equal to E x prime. We have already seen that E x prime is equal to 0. So, E x also has to be equal to 0. E y, I have written this equation. E y is equal to gamma E y prime plus v b z prime. This is what I write here. E y is equal to gamma E y prime plus v b z prime. Here only E y prime is non-zero quantity. E b z prime is 0. That is what we have said earlier. E y prime is equal to E naught. So, this becomes just gamma times E naught. Gamma we know is 1.25. So, this becomes E is equal to 1.25 E naught. Of course, there is a prime. Similarly for E z, we write this equation because this is 0. This is 0. Therefore, E z is equal to 0. So, what we have seen is that only the electric field, the y component would be present out of the three electric fields. E x will be 0. E z will also be 0, but E y would appear to be changed in principle. E y will turn out to be larger than E naught prime. It will become 1.25 times E naught prime. But that is not the complete story because what I have calculated are only the electric field. I must also calculate the magnetic field to find out if there is a magnetic field in S frame. In S prime frame, there was no magnetic field, but in S frame, there could be a magnetic field. So, the components of the magnetic field can be derived or can be found out by using these equations. Let me just remind you these equations which I have written here in this piece of paper. These are my equations. I have to use an inverse transformation. I would use this set of equations. B x is equal to B x prime as we have said along the x direction, which is the relative motion velocity direction between the frames. The fields do not change. So, B x remains equal to B x prime. B x prime was anyway equal to 0. So, B x is equal to 0. This is what I have written here. As far as second equation is concerned, B y prime is equal to gamma B y prime minus B y c square E z prime. E z prime is 0. B y prime is equal to 0. So, this is also equal to 0. So, as far as x component and the y component of magnetic fields are concerned, they are 0 in this frame also. But let us look at B z, which is non-zero. B z, if you look back in this particular paper, B z was equal to gamma B z prime plus V by c square E y prime. Same thing I have written here. B z prime is 0, but E y prime is not 0. It is actually equal to E naught prime. Gamma is equal to 1.25. V, I know is 0.6 c. So, this is 0.6. This c will cancel one of those squares. So, I will get 0.6 multiplied by E naught prime divided by c. So, if I just calculate this number, this turns out to be equal to 0.75 E naught prime by c. So, what I find that in this particular frame of reference S, the electric field was equal to 1.25 times E naught prime, which we have just now written earlier. And you have B z, which is equal to 0.75 times E naught prime divided by c. So, what I see that in S frame of reference, the charge or the person in the frame will also experience a magnetic field in the z component direction pointing out in the plus z direction, which will be equal to 0.75 times E naught prime by c. So, the field which was purely electrical in S frame of reference turns out to be partly electrical, partly magnetic in S frame of reference. So, what I have written here? We thus see that the electric field in S is 1.25 times the same in S prime. Moreover, a magnetic field would also be felt in S frame pointing out in plus z direction. This is what comes out from the relativity. Now, let us look at the forces. If I look at the force in S frame of reference, because there was only an electric field and also, it has been given that the charge is at rest, but anyway there is no magnetic field there, which has not been given. So, we can write the force, which I can write as E y. Once I write E y and because I am sorry, let me write the force, not the field. Field has been given. I am writing F y. This will be given by just E times E y, because that is the only force, because there is electric field in the y direction and there is no magnetic field. Charge is anywhere at rest. So, let me write Q, because Q is the value of charge, which has been given to me. So, the force will be just given by Q E y purely electrigraphy force, which will be pointing out in the y direction. So, this is what I have written. F prime is equal to Q E naught prime J. This I have written in the vector form. Of course, i, j, k point out in the same direction. They just give you unit vectors irrespective of the frame. They give the unit vectors in directions pointing out along the y direction, x direction, y direction and z direction and because this is j. So, therefore, they are pointing out in the y direction. Now, let us evaluate the force on this charge in S using the calculated fields. Now, as far as S frame is concerned, there is also a magnetic field and both the charge is at rest in S, prime frame of reference. Charge is not at rest in S frame of reference, because S moves relative to S. Therefore, the charge also moves relative to S. Therefore, if there is a magnetic field in S, the magnetic field will also cause a force on this particular charge. So, let us calculate that particular force. Now, we are looking at the force on the particle. So, let us first look at the speed of the charge, because the charge is at rest in S, prime frame of reference. So, whatever is the speed of S, prime in S frame of reference, same would be the speed of the charge. So, u, which is the speed of the charge, as seen in S frame of reference, will be just 0.6 c and it will be pointing out in the i direction, because S frame of reference, rather S, prime frame of reference moves in S with a speed of 0.6 c in plus x direction. So, therefore, this will be u. I can write the force. Force will be given by q times e, electric field we have already seen is 1.25 times e naught prime plus v cross b, v is 0.6 c i. We have already seen that there is a magnetic field pointing out in plus direction plus z direction and the magnitude of that particular field is 0.75 e naught prime by c and because it is in plus z direction, I have written k. So, this will be the entire Lorentz force on this particular particle. This is because of the electric field. This is because of the magnetic field. First term I keep as it is. Let me look at this cross product. This is i cross k. So, i cross k will give me minus j. I just multiply 0.6 c with 0.75. This c will cancel with this c. You will get minus 0.45. This minus sign is because i cross k is minus j. So, this gets subtracted from this and I find that the force which we experienced in charge in s frame of reference will be 0.8q e naught prime, 0.8q e naught prime j. So, this piece of paper gives me what are the field values that I see, what are the speed of this particle and what will be the force on this particular charge. Remember, this is q. Of course, I expect that this force must obey the transformation equations that we have found out. In s frame, the force is in the y direction. So, it is an s frame of reference. So, let us look only at the equation corresponding force transformation corresponding to the y component. And if you remember, if charge happens to be at rest or if the particle happens to be at rest in one of the frame, the transformation equation is comparatively simple. So, I will use those simple equations. This is very obvious here because it is in the prime frame of reference that the charge is at rest. So, force, the y component of the force will be just given by f y prime by gamma and gamma is 1.25. 1 upon 1.25 is just 0.8 and this is what I have obtained that the force has become 0.8 times the force on the charge in s frame of reference. So, this obeys the force transformation equation as I would have expected. Now, let us try to calculate the fields in s double prime frame of reference. And let us, I mean I could have gone either from s frame of reference or I could have gone from s frame of reference. So, at the moment, I am transforming from s frame because now I know the fields both in s frame as well as in s frame of reference. So, I could have used any transformation. Let me first calculate the fields starting from s frame of reference where I have calculated the fields just now. At later part, I will also transform from s frame of reference to see that we are getting everything right which we must get. We must test ourselves that whatever we are doing is real turning out to be correct. Now, if I go from s frame to s double prime frame of reference, I go back to this particular piece of paper here. This is s, this is s double prime. We have said that according to an observer in s frame of reference, s double prime frame moves with a speed of 0.8 c. So, if I have to, if I know certain quantities in s frame, I have to transform into s double prime frame of reference. Therefore, I will use direct transformation. And I will use a direct transformation with a v is equal to 0.8 c because this is the relative velocity between the frame. So, remember the symbol v was reserved for relative velocity between the frames. So, here I will use v is equal to 0.8 c because that is the relative velocity between s and s double prime. And I will take v is equal to plus 0.8 c and I will use a direct transformation because the information is known as s frame and I want them to be in s double prime frame of reference. Now, again v is equal to 0.8 c gives me a clean number for gamma and this gamma happens to be 5 by 3. This also we have done in many of our earlier examples. We have used corresponding to 0.8 c, gamma turns out to be equal to 5 by 3. Now, s double prime is equal to x. There is no problem because as I have said along the relative velocity direction, the fields do not change. So, relative velocity is along the x direction. So, the x component of the fields do not change. So, e x double prime is equal to e x is equal to 0. Now, let us look at e y double prime. Here I am going to use the direct transformation equation as I have mentioned earlier. If I look at this paper, earlier when I went from s prime to s prime, I use this equation. When I go from s to s double prime, I use these equations because now I am using a direct transformation. So, I use e y prime is equal to gamma e y minus v v z. And remember in s frame, we have nonzero e y and nonzero v z. Both are nonzero. So, I should calculate e y prime. This is what I have done here. E y double prime is equal to gamma e y minus v v z. We have just now calculated the electric field in s frame, which is 1.25 times e naught prime minus v. v is the relative velocity between the frames, which is 0.8 c. v z is the magnetic field as seen in s frame or the z component of the magnetic field, which is 0.75 times e naught prime by c. This c and this c will cancel. So, here you will get 0.8 multiplied by 0.75 e naught prime, just sort of calculate the simple number. You will get 13 by 12 e naught prime. So, what we will find out that an observer in s double prime frame of reference will notice an electric field of 13.12 e naught prime. So, let me write it here. In s double prime frame of reference e y double prime turns out to be equal to 13 by 12 e naught. Let us look at e z double prime. e z double prime is here. Gamma e z plus v v y. e z is 0 in s frame. v y is 0 in s frame. So, e z double prime is equal to 0. Therefore, the only field, only, only component of electric field that you see is only along the y direction, which happens to be 13 by 12 e naught prime, which is of course, larger than what you have seen in s prime frame of reference. But as I have said, this is not the complete story. I should also calculate the magnetic fields. Now, let us calculate the components of the magnetic field s double prime can now be found out using the field values in s because I am using a transformation from s frame. Along the x direction no problem, v x double prime is equal to v x is equal to 0. Let us look at the y component. I am using a direct transformation. Remember, this is equal to gamma v y plus v by c square e z. v y is 0, e z is equal to 0. This is 0. So, x and y component of the magnetic fields are 0, as they were also 0 in s frame. Now, let us calculate v z double prime, the z component of the magnetic field in s double prime frame. v z double prime is equal to gamma v z minus v by c square e y using the direct transformation. Gamma is equal to 5 by 3. I have put 5 by 3. The z component of the magnetic field we had calculated is 0.75 times e naught prime divided by c. Electric field we have calculated 1.25 multiplied by e naught prime by c. This is a relative velocity 0.8 c. This c cancels with one of the squares. So, this just remains e naught prime by c. Just calculate this number. This turns out to be equal to minus 5 by 12 e naught prime by c. So, we see that now in s double prime frame, the magnetic field appears to be in minus z direction because there is a negative sign here. So, an observer in s double prime will feel that in his field, there is a field, electric field in the y direction and a magnetic field in minus z direction. Let us calculate the forces and see whether they obey the transformation law. So, you have said v the c that s double prime has the magnetic field. v the c that in s double prime, the magnetic field would be felt in negative z direction. In order to calculate the force on charge q in s double prime frame, we have to find the speed of s double prime because what has been given are the speeds of frame s prime and s double prime in s. What has also been given is that the charge is at rest in s prime frame of reference. I do not know the speed of the charge. See, from s to s prime, I can find out because if the speed of the charge is point of the s prime frame is 0.6 c and the charge is at rest in s prime, therefore, obviously u is equal to 0.6 c. But here in this particular case, I have to find out by using a velocity transformation. See, I know what is the speed of the frame s double prime in s. I also know what is the speed of the charge in s. I have to find out what is the speed of s in s double prime. I have to use a velocity transformation. Information about the speed of the charge and the speed of the frame has been given to us in s s frame. If I want to find that information in s double prime, s double prime frame, because I have to calculate now the force in s double prime frame of reference and because there is a magnetic field in that frame, therefore, force will depend on what is the speed of the charge carrier in that frame. I must find out the speed of the charge in s double prime frame of reference and for that I must use a velocity transformation, which I am using in the next transparency. This is the standard velocity transformation equation, which we have used in many of the examples earlier. u x minus v divided by 1 minus v u x by c square. See, remember u x is the x component of the particle of the speed of the velocity of the particle. The particle is the charge, which moves with a speed of 0.6 c in s frame of reference. So, u x is equal to 0.6 c. v is the relative velocity between the frame. I want to transform from s to s double prime and that speed is 0.8 c. So, v because 0.8 c divided by 1 minus v, which is 0.6 c, I am sorry 0.8 c, u x which is 0.6 c, c square will cancel with the c square, you get 0.6 multiplied by 0.8, which is 0.48. So, this because 1 minus 0.48, which will give you minus 0.2 divided by 0.52. So, according to an observer in s double prime frame, the charge is moving in minus x direction, which is sort of sensible, because in s frame, the frame s double primes moves with a larger velocity than s prime. Therefore, whatever is at rest in s prime would appear to be moving backwards. Therefore, it is expected that u x double prime will turn out to be negative, which it need turns out to be. Now, as far as the y and z components are concerned, they will give me 0. So, I need not bother about it, because u y is 0, u z is 0. As far as the charge is concerned, it moves only along the plus x direction in s frame. These components are 0, only the x component is non-zero. I do exactly the same equation. I use the trans the Lorentz force equation in s double prime frame of reference. I write the force, force equal to q times e, which I have just now calculated 13 by 12 E naught prime. V, which I have just now calculated is minus, let us remember, you know that this was minus a speed, this was minus 0.2 divided by 0.52. But the magnetic field was also minus 5 by 12 E naught prime by c. So, these two minus makes it plus. So, this becomes 0.2 divided by 0.52 c in i direction cross 5 by 12 E naught prime by c in k direction. I take the cross product i cross k, this will give me minus a. So, here there will be a minus sign. Then you just simplify, multiply these particular things and you get f double prime is equal to 12 by 13 q E naught prime j. So, in s double prime frame of reference, the charge, the force on the charge will be given by 12 by 13 q E naught prime j, which remember is smaller than q E naught prime. Remember, we have said that this force is seen to be largest in a frame of reference in which the charge, the particle happens to be addressed. So, as you can see that these two forces are smaller than the force that this particular particle would have experienced in s prime frame of reference. Now, let us confirm that this follows from the force transformation law. So, let us look at the transformation of the x component of the force. Here, when I am transforming from s prime to s double prime frame of reference, particle is neither addressed at s prime frame of reference nor at s double prime frame of reference. So, I cannot use those short equations. I have to use the complete equations. And complete equations as far as the x component is concerned is here. There is little more involved, but nevertheless we can do because I know all the speeds. So, let us calculate as far as f x is concerned, this is 0.  So, I am trying to calculate it in the next transformation. As we have seen, f x is equal to 0. The charge also moves in s frame only along the x direction. Therefore, u y is equal to 0. The force is only along the y direction. So, f z is also equal to 0. Velocity is only along the x direction. So, u z is also equal to 0.  Of course, u z is also equal to 0. The dot product f dot u will be 0. So, this will give me the x component of the force to be equal to 0. This anyway I had expected. It is the y component which is more interesting which let us write it here. Complete equation f y divided by gamma 1 minus v u x by c square as far as f y is concerned. This is 0.8 q e naught prime. This is what I have written as far as the frame s is concerned. u x the speed of the charge is along the x direction which is 0.8 c. Gamma we have already said is 5 by 3. So, in this particular equation gamma is 5 by 3. So, I will write this as 3 by 5 because this is 1 upon gamma. So, this is 3 by 5. For f y, I have written 0.8 q e naught prime. So, this is 0.8 q naught prime divided by 1 minus v into u x which is 0.6 into 0.8 which you must 0.48. Just substitute you will find that the y component of the force indeed turns out to be 12 by 13 q e naught prime as we have seen it earlier in this piece of paper. I have written that f double prime is 12 by 13 which I also get from the force transformation equation which I had expected. Now as far as f double prime is concerned, this anyway turns out to be equal to 0. We thus see that the force transformations are obeyed as was expected. So, I am just summarizing all the fields and the forces that I have got in all the three frames. This is an s frame from which we had started. We had written the speed of the particle was 0. B, the magnetic field was 0. The electric field had only y component which is e naught prime. The force on the particle was q e naught prime. Other electric field and the force components were 0. If you go to s frame of reference, things change. u x, the particle is no longer at rest. It is speed is 0.6 c. The particle also experiences a z component of the magnetic field which is in the plus z direction, the magnitude of which is 0.75 e naught prime by c. It also experiences an electric field in the y direction which is now somewhat larger than what was seen by s frame, s prime frame. This is equal to 1.25 e naught prime and the force on this particular charge will turn out to be 0.8 q e naught prime which is the complete Lorentz force, the force which is because of electric field as well as because of the magnetic field. Other velocity fields and the force components will all be 0. Now, let us write in s double prime frame of reference. In s double prime frame of reference, I have to calculate the speed of the charge by using the velocity transformation and that I found out to be equal to u x double prime was equal to minus 0.2 divided by 0.52 c. In this particular frame of reference, there was a z component of the magnetic field but it was pointing out in the negative z direction which was minus 5 by 12 e naught prime by c. And there will be an electric field as usual in the y direction and the magnitude of that will be 13 by 12 e naught prime. So, as we have seen that the electric field also has changed, magnetic field also has changed and the force on the particle is 12 by 13 q e naught prime. The forces is also changed but as we have seen that these forces obey the force transformation law as it was expected. So, I said other velocity field and force components are 0 in this particular frame of reference. So, this is just a summary of what will be the fields which will be seen as s double prime frame of reference and also the forces. As we can see that a field which happened to be purely electrical turns out to be electrical and magnetic, a combination of electric and magnetic field both in s frame and s double prime frame. As you can see the picture is very different.  It depends on the frame from which you want to look into, it could be a combination of them. Before we close, let me do one more thing. Let me try to make a transformation directly from s prime frame to s double prime frame of reference. That is what we have said that where I have to calculate the field in s double prime frame of reference, either I could have started from s or I could have started from s prime. What I did, I started from s frame to s double prime frame of reference. The advantage here was that I knew the relative velocity between the frames but I did not know the charge velocity. In s prime to s double prime, if I calculate, I will not know the relative velocity of the frames because that has not been given to me. I have to use my velocity transformation and find it out. But the charge I know is at rest in s prime frame of reference and the advantage is that because the charge is at rest, so I can use that simplified the force equation. Let me just do this particular thing quickly. So, before we close this example, let us attempt a transformation from s prime to s double prime frame without going through s. So, if I go from s prime frame to s double prime frame of reference, I must know and if I want to use the direct transformation, I must know the speed of s double prime frame of reference in s prime frame of reference. As I said for this, I have to evaluate gamma between s prime and s double prime frame. For this, we have to find out the speed of s double prime in s because I am transforming from s prime to s double prime frame of reference. So, I must know what is the speed of s double prime in s prime frame of reference and information being given in s prime and transforming to s double prime, I would use a direct transformation. However, I need not calculate this because I have already calculated this in a way. I was told that the charge at rest in s prime frame of reference, we have already calculated the speed of the charge in s double prime frame of reference, which was minus whatever it is. So, remember what is the speed of the charge in s double prime frame will also be the speed of s prime frame in s double prime frame of reference because the charge is at rest in s prime frame. So, therefore, whatever I had calculated 0.2 or 0.52 will be the speed of s prime frame in s double prime frame of reference. But if I want to use direct transformation, I must know what is the speed of s double prime in s prime frame of reference, which will just be opposite to the sign. Hence, the speed of the s double prime in s prime frame will be given by v is equal to plus 0.2 divided by 0.52 c because when I had used minus, that was the speed of s prime in s double prime. I want to find out what is the speed of s double prime in s prime, which is just opposite to the sign. If I am going this way, the speed is like this. If this is at rest, the speed is the other way. It is as simple as that. I calculated gamma using this. This turns out to be 13 by 12. Now, I can make electric field transformation as far as x component is concerned, it is straight forward 0. I am using direct transformation. I use gamma is equal to 13 by 12, E y prime minus V B z prime. This will just be given by 13 by 12 E naught prime as I expected. E z prime will turn out to be equal to 0 as I expected. So, I could have directly gone from s prime to s double prime and calculated electric fields without any mistake. Magnetic field, s component is 0, y component is also 0. Let us go to the z component. Z component is V z prime, which happens to be 0 minus V by c square E y prime. V is given by 0.2 divided by 0.52 c. This c will cancel here. The field as far as s prime frame is concerned is just E naught prime. I put it E naught prime. Just work it out. I get exactly minus 5 by 12 E naught prime by c as I had expected. So, I could have gone from s prime to s double prime also or s to s double prime makes no difference. We thus get the identical result as expected. So, in conclusion, we had used another method to derive perpendicular magnetic field transformation and also worked out an example of electric and magnetic field transformation. Thank you.