We conclude our course today with the discussion of a question that we had asked earlier that take ethanol we say that there is a certain kind of splitting of CH3 proton resonances because of the CH2 protons coupling with CH2 protons. Why is it that there is no splitting of CH2 resonance because of coupling of the CH2 protons? Is there no coupling? That is what we generally think right when we talk about NMR, I think it is even casually said that protons with same chemical shape do not couple with each other perhaps that statement has been made in some course or the other and that statement is not quite accurate. There is no reason why protons with same chemical shift should not couple with each other. After all the basis of coupling is that they are magnets. So why will they not couple with each other? So today let us see how we can perform a time independent perturbation theoretical treatment of coupling of protons with same chemical shift and whether that leads to any kind of splitting in the NMR spectrum of such systems. So what we are discussing today really is no splitting for A2 systems. To start our discussion as usual we are going to write the Hamiltonians and we are using perturbation theory. So our job is to first write the unperturbed Hamiltonian and then write the perturbation correction to the Hamiltonian. So can you help me with this? What is the unperturbed Hamiltonian going to be in case of A2 system? Let us remind ourselves what it was for the AX system. Yesterday we have discussed the AX system. What was the Hamiltonian for AX system? Minus gamma B0 1 minus sigma A IZA right and then what was the next term? Minus gamma B0 1 minus sigma X multiplied by IZX operator. In this case what is the difference from AX system? There we have two kinds of shielding constants right sigma A and sigma X here since it's A2 in both the terms we have to use sigma A, there is no sigma X right, if that is the case what I'll do is instead of writing IZA and IZX there are still two nuclei right. So I'll write IZ1 and IZ2 and I hope you don't have a problem if I write it like this. Do we agree that this is the unperturbed Hamiltonian? And by the way in case I have not said it earlier this entire discussion is from Macquarie and Simon's book. It is also there in Grebiel's book but I find Macquarie and Simon to be very easy to understand in this part so you can follow that book. Are we all okay with the unperturbed Hamiltonian right? H0 is minus gamma B0 into 1 minus sigma A multiplied by IZ1 plus IZ2 where 1 and 2 denote the two nuclei both of which are of A kind. What will be the perturbation term? First order correction to the Hamiltonian it will be like earlier HJ, this time I will not write JAX, I'll write HJAA divided by h cross square multiplied by what? I1.I2 is that right? So I might as well expand since we discussed it yesterday I'll write like this, IX1.IX2 plus IY1.IY2 plus IZ1.IZ2. This here is my first order correction to the Hamiltonian okay and of course now what is the next step? We only found out structure for a note. Now here these look like this right? So I am not going to go right to the point of the problem but the clothes are going to be like the dunwalli, for fun, right? So earbuds and everything. So my question here is what's left over is both l0 and l3 because it's already different detail and if you understand the equation I'm going, I think you guys unperturbed wave functions, yesterday I wrote Psi, so today let me write Phi, just to be in line with the aquarium Simonscope, there is no other reason, Phi 1 will be as usual, now I will write Alpha 1, Alpha 2, yesterday we had written Alpha A, Alpha X, right, so here I will write Alpha 1, Alpha 2, and let me write Phi 4 as Beta 1, Beta 2, what is Phi 2 and what is Phi 3, what was Phi 2 yesterday, for AX system what was Phi 2, Beta 1, Beta A Alpha X, and Phi 3, Alpha A Beta X, can I keep the same wave functions just substituting A and X by 1 and 2, is there a yes or no, yes, no, why, why do we take a linear combination, so we come back to something that we learned earlier, remember indistinguishability, yesterday we were talking about AX system, there was a difference between the two nuclears, right, they had, they experienced different kinds of fields, so it was, I could distinguish between A and X, now I cannot, and since I cannot, then we have to go back to our old friends the linear combinations of the wave function, okay, same thing that we did in electronic spectroscopy, it's just that there we were talking about electronic spins, here we are talking about nuclear spins, that's the only difference, so this is 1 by root 2, Alpha 1, Beta 2, minus Beta 1, Alpha 2, this one is 1 by root 2, Alpha 1, Beta 2, plus Beta 1, Alpha 2, all right, what is my job now, my job is to find the energies of the four levels denoted by the wave functions 5, 1, 5, 2, 5, 3 and 5, 4 and work out the transitions and when we do that, as you'll see something new will crop up that we did not discuss, that we did not need to discuss yesterday, so these two wave functions 5, 1 and 5, 4 are exactly the same as the wave functions that we handled yesterday, so there is no reason why their energies should be of any different form compared to what we had yesterday, agreed? Yesterday also, Psi 1 was Alpha 1, Alpha 2, right, Psi 4 was Beta 1, Beta 2, so whatever expression we got for their energies, we should get similar expressions here, you can do the math, it'll be the same thing, so maybe I'll just write that, where do I write, maybe I'll write here, I'll keep that part available, what will be the energy of Phi 1? What was the expression yesterday? Yes, minus H cross gamma B0 multiplied by, yes, 1 minus, what was that? Alpha A plus Alpha X divided by 2, isn't it? Sorry, why am I seeing Alpha, sorry, Sigma, sorry, my mistake, Sigma A minus Sigma X divided by 2, was that right? Today is there any difference between Sigma A and Sigma X, so what is Sigma A plus Sigma X divided by 2, Sigma A? So now I'll get 1 minus Sigma A, that's it, what else did we do? We wrote this as nu 0, actually H nu 0, when nu 0 is the Larmor frequency of a Bayer proton, so if you want to write it in terms of frequency, then this is going to correspond to frequency of A nu, yes, all right, what was the correction term? What was the first order correction? H, J, there it was AX, here it is AA divided by 4, okay, I'm not doing the math, please do it yourself, you'll come to the same result, the math is exactly similar to what we did for AX yesterday, with one less complicating factor there is no Sigma X, there is no JX, everything is A, there is no X, okay, so E1, I hope you can agree on that, what is E4? Maybe like yesterday we'll write the same thing, E4 will be just this thing with a plus sign, what about this, will this become minus? No, so both alpha alpha and beta beta states actually get destabilized as a result of coupling, so the second term we still have a plus sign, the only difference that we'll have as we saw yesterday is that in case of level 1 we'll have a minus sign here, there'll be a stabilization, in case of level 4 there will be destabilization and we'll have plus 1. Now let us see what is going to be the scenario for E2 and E3, E2 and E3 of course should be different from what we obtained for the AX case, right, because the wave functions are different, let's see what it is, so this is where I'll write the energies and this is where I'll work it out, so let's work out E2, 0, how do I get E2, 0? I make this Hamiltonian operate on phi 2, right, so what do you get then? Minus gamma B0, 1 minus sigma A, IZ1 plus IZ2, this whole thing operates on 1 by root 2 alpha 1 beta 2 minus beta 1 alpha 2, what do I get? What do I get? How many terms do I get? IZ1 operates on alpha 1 beta 2 and on beta 1 alpha 2, so 2 terms there, IZ2 operates on alpha 1 beta 2 and beta 1 alpha 2, 2 terms there, but one thing I hope you can understand is that since I'm using IZ it'll always be eigenvalue, isn't it? It'll always be an eigenvalue equation and eigenvalues are going to be either plus H cross by 2 or minus H cross by 2, so what I'll do is I'll write these eigenvalues here and I'll write the wave function here, 1 by root 2 is common, let's not bother about that, that will come anyway, okay. So what happens when IZ1 operates on alpha 1 beta 2, how much do I get? I get back alpha 1 beta 2 first of all, what is the eigenvalue? Yes, little louder, IZ1 operating on alpha 1 beta 2, so beta 2 is a constant as far as IZ1 is concerned and what do you get when you operate IZ1 on alpha 1? H cross by 2 alpha 1, right, so that's why I've written alpha 1 beta 2 there and the eigenvalue is H cross by 2. What happens when IZ1 operates on beta 1 alpha 2, minus H cross by 2 and I write this one here minus beta 1 alpha 2, is that okay? Next is IZ2 has to operate on alpha 1 beta 2 and minus beta 1 alpha 2, IZ2 operating on alpha 1 beta 2 what do you get? What is the function? I get back alpha 1 beta 2 and what is the eigenvalue? IZ2 operating on alpha 2 and beta 2, minus H cross by 2, excellent. Now when IZ2 operates on minus beta 1 alpha 2, I have minus beta 1 alpha 2, this I can close, what is the eigenvalue? IZ2 operating on beta 1 alpha 2 I've taken the minus there already, so plus H cross by 2, so what do I have here? I have 2 into the wave function, isn't it? So it is an eigenvalue equation, but what is the eigenvalue? 0, is that right? Eigenvalue is 0, is that surprising? First time I was surprised, why is it not surprising? I do so much of math and then get eigenvalue 0, why is it not surprising? I should be surprised. See earlier what did we have? You had alpha and beta, right? So stabilization of one, destabilization of one was not the same, so you had some net energy. In this case, one is alpha, one is beta, both are equivalent. So stabilization of one is exactly offset by the destabilization of the other, energy is 0, okay? So what we learn is that your energy of, well at least E0, let me write, of level 2 that is 0, okay? Akansha, I'm sorry, can you say that again? How did I get this? Let's do one term then, open which bracket? No, we did everything. So what do we have? If you open the bracket, you have I, I'll just write I1 and let me call this, I don't know, chi1 and chi2. So I'm going to have, this is I1, this is I2, I have I1 chi1 minus I1 chi2 plus I2 chi1 minus I2 chi2, is that right? And then let us look at one of these terms. What is I1 chi1? That is your, you can write like this, I'm not writing 1 by root 2 here, beta2, IZ1 alpha1, isn't it? Because IZ1 will not operate on beta2, beta2 will be a constant as far as it's concerned. What do I get from here? IZ1 alpha1 is h cross by 2 alpha1, so you get back h cross by 2 alpha1 beta2. See h cross by 2 alpha1 beta2, that is how we evaluated every term. Yes, each term is h cross by 2, but then it's not always h cross by 2. If it is beta wave function, it will be minus. So that's why in two cases it is plus h cross by 2, in two cases it is minus h cross by 2, that is why it cancels off. Are you satisfied? You understood, very good. She doesn't look very convinced. Which multiplication? So that is what I just explained. This part you're okay, right? So I have to do it term by term, isn't it? What is the first term? First term is IZ1 operating on alpha1 beta2. So let me explain in a different way now. So what I have is IZ1 operating on alpha1 beta2. That is the first term, you agree? What will be the second term? IZ1 operating on minus beta1 alpha2. So minus IZ1 operating on beta1 alpha2. What is the third term? IZ2 operating on alpha1 beta2. What is the last term? Minus IZ2 operating on beta1 alpha2. Now what I am saying is IZ1 operates on alpha1, but not on beta2. So beta2 is a constant as far as this operator is concerned. So you can take beta2 out. Here also, you can take alpha2 out. In this case, take alpha1 out. And in this case, take beta1 out. What is IZ1 alpha1? Yes. So that's where we get it. You're right. So let me, I think I made a mistake, fine. So let me write like this. You have to take into account 2. Then it falls in place, right? It will work out. Fine. So we get 0. Work it out for phi3. You will get 0 once again. So now, what is the picture that we get for the uncoupled scenario? This is your phi1. This is phi2 and phi3. This is phi4. What is the energy gap here? This is 0. This is your minus nu0 multiplied by 1 minus sigma a. What is that? It is 0. Well, then h multiplied by that. So essentially this is h nua, isn't it? If I just write in terms of frequencies, this is nua. What about this? This is 0. This is plus nu0 multiplied by 1 minus sigma a. That is once again, if you write in terms of frequency, this is nua. So in the uncoupled scenario, you expect to get one line at the resonance of a. Now, what is the correction term? Now, to do the correction term, again, we have to remember what we get. So tell me ix operating on alpha. What do I get? ix operating on alpha? Yes, h cross by 2 multiplied by beta. It's not an eigenvalue equation. Iy operating on alpha, what do I get? Yes, Iy operating on alpha. This is what we discussed yesterday. Ih cross by 2 multiplied by beta. Iz operating on alpha, that we know it is h cross by 2 alpha. That is the only eigenvalue equation. What happens when ix operates on beta? What do you get? Iy, this is something we discussed yesterday without derivation. This is what comes from the spin matrices. Since we do not really talk about, we do not have the scope to get into relativistic quantum mechanics and all that, we have to take this action. Iy operating on beta gives us, what is this one? Minus. So this is the thing to remember. Minus ih cross by 2 alpha. Iz operating on alpha, that of course we know is minus h cross by 2, sorry, why am I writing alpha? Iz operating on beta, that of course is minus h cross by 2 beta, alright.  So to make our job easier at the end, let us do something. Let us see what is ix 1, ix 2 operating on alpha 1 beta 2. What is Iy 1, Iy 2 operating on alpha 1 beta 2 and so on and so forth. We will just write down those terms and then we will take it from there. So ix 1, ix 2 operating on alpha 1 beta 2, that will be ix 1 alpha 1 operated, multiplied by ix 2 alpha, you know, beta 2. What do I get? ix 1 alpha 1 is what? h cross by 2 beta 1 and ix 2 beta 2 is h cross by 2 alpha 1 or 2, alpha 2. So I get h cross square by 4 beta 2, alpha 2. Is that right? So this is what is going to happen throughout. As long as you are using x or y, 1 and 2 will get interchanged. As long as you use z, they will not get interchanged and it will always be h cross by 4, whether there is a plus sign or minus sign that we have to see. ix 1, ix 2, alpha 1 beta 2, that is done. What is your ix 1, ix 2, beta 1 alpha 2, what will it be? Now I think we can work it out mentally. ix 1, ix 2, beta 1 alpha 2, what will it be? h cross square by 4 alpha 1 beta 2. Is that right? Then iy 1, iy 2, alpha 1 beta 2, what will that be? Iy 1, Iy 2, alpha 1 beta 2. So first of all it will become beta 2, alpha 1. Then you have h cross square by 4 also. What is the sign? Plus, i into i is minus 1 and there is a minus 1 already. Oh, sorry, sorry, sorry. I changed the sequence as well as the indices, beta 1, alpha 2. What is iy 1, iy 2, alpha 1, alpha 2 operating on alpha 1, alpha 1 beta 2 have already done. So beta 1, alpha 2. What will it be? h cross square by 4 alpha 1 beta 2, plus or minus? Plus, iz 1, iz 2, alpha 1 beta 2. What is that? Minus h cross and this time there is no exchange, alpha 1 beta 2, h cross square by 4 alpha 1 beta 2. And what is iz 1, iz 2 operating on beta 1 alpha 2? iz 1, iz 2 operating on beta 1, alpha 2. What do I get here? Did I write the minus sign here? Minus h cross square by 4 beta 1 alpha 2. This is what alpha 1, alpha 2, alpha 1 beta 2. What will we need in order to work out the correction? Now, what is the expression? What is the expression for the first order correction to energy? First order correction is psi 0, first order correction to Hamiltonian, psi 0 integrated over all space. This is what we have learned from perturbation theory. So essentially what we will try to do is we will try to evaluate this h1 psi 0 and then let's multiply by psi 0 integrate over all space. What is h1 psi 0? Let us see. We are talking about phi 2. What is h first order phi 2? That will be hjAA. Now, what we have seen there is that no matter which term we use, we will always get either plus or minus h cross square by 4. So I can take h cross square by 4 outside the bracket. So that h cross square and this h cross square will cancel. And you are left with hjAA divided by 4. I'm trying to evaluate this. What happens when this first order correction to Hamiltonian operates on phi 2? Phi 2 is alpha 1 beta 2 minus beta 1 alpha 2. Now, take any of these operators, operate on any of these terms, you always get either plus or minus h cross square by 4. So I hope it's not very difficult to see that h cross square by 4 will be common outside the bracket. And the moment we do that, this h cross square, that h cross square will cancel. You will be left with hjAA divided by 4. Now that will be multiplied by whatever. So once again, let us try to do it like this. Here I'll write the numbers. Here I'll write the wave function. So ix1, ix2 operating on phi 2. 1 by root 2 is common anyway. So I'll write it here. ix1, ix2 operating on alpha 1 beta 2. What do I get? Alpha 1 beta 2. Why did I erase it? The first thing I erased. Is that right? So h cross square by 4 I have taken out. So here I get 1. So if I write it that way, again I'll land in the same problem, isn't it? So let's not try to do that. I've understood where the problem was. The problem was in my writing. 1 by root 2, okay. But I can take h cross square by 4 outside the bracket. There's no problem with that, isn't it? Sorry? Okay, let's see. We'll just do it. 1 by root 2 you can take. That's not a problem. It'll be 1 by 2. Fine. What are you saying? Right now I'm only operating. I'm not integrating yet. It is 1 by root 2. It'll become 1 by 2 when you write multiply also. Okay. So first I get beta 1 alpha 2. Then what do I get after that? Beta 1 alpha 2 I have written. Next is ix1, ix2 operates on minus beta 1 alpha 2. Wait, say which one you are operating. Iy1, Iy2 operates on alpha 1 beta 2. What do I get? You have plus or minus. We need agreement on that, plus or minus. Don't forget we have taken h cross square by 4 outside the bracket. Okay. ix1, ix2 operating on alpha 1 beta 2 has given us beta 1 alpha 2 multiplied by h cross square by 4. Then ix1, ix2 operating on beta 1 alpha 2 also gives us h cross square by 4 beta 1 alpha 2 but there's a minus sign here already. Right? That's why we have written minus alpha 1 beta 2. Next is iy1, iy2 operating on alpha 1 beta 2. What do I get? h cross square by 4 beta 1 alpha 2, plus or minus, plus, h cross square by 4 has gone out. So beta 1 alpha 2. Next one iy1, iy2 operates on beta 1 alpha 2. What do I get? Alpha 1 beta 2 plus sign or minus sign, minus. What is it? Beta 1 alpha 2? Alpha 1 beta 2. Then what is the next one? Iz1, Iz2. Right? Operates on alpha 1 beta 2. What do I get? Iz1, Iz2 operates on alpha 1 beta 2. Minus alpha 1 beta 2. Last, Iz1, Iz2 operates on beta 1 alpha 2. Minus but then there's another minus already. Right? Plus beta 1 alpha 2. Right? What do I have then? What do I have?  Right? What was the wave function? Alpha 1 beta 2 minus beta 1 alpha 2. Right? So this is how I'll write it. Minus phi h j a a divided by 4 into 1 by root 2 alpha 1 beta 2 minus beta 1 alpha 2. Is that right? And what is that wave function? 1 by root 2 alpha 1 beta 2 minus beta 1 alpha 2. It is phi 2. So I can write phi 2. So then, what is the first order correction to E2? You have to let it be the first order left multiply by phi 2. Integrate over all space. What do you get? Integral phi 2 star phi 2. What is it? That is 1. So minus phi h j a a by 4. So what we get is E2 is then 0 minus phi h j a a divided by 4. And that is a different result. From what we got yesterday for the second energy level, is it not? In that energy, yesterday what we saw is alpha alpha and beta beta were destabilized by h j x divided by 4 and alpha beta and beta alpha were stabilized by the same amount. That is not the case here. Alpha alpha and beta beta are still destabilized by h j a a by 4 this time. But what we see is alpha beta minus beta alpha is stabilized by phi h j a a by 4. So in fact from there itself, perhaps we can figure out what will be the first order correction to energy of phi 3. The total change in energy should be 0, isn't it? Stabilization has to be equal to destabilization. So when do you get 0? What will be the amount of stabilization of E3 is 0? It will be h j a by 4, isn't it? Because 2 into h j a by 4 plus h j a by 4 that is equal to 3 h j a by 4 that added to minus 3 h j a by 4 is equal to 0. But let us see if we get that. So this is the same exercise but this time I want to use phi 3 instead of phi 2. Can you tell me what is h first order operating on phi 3? Phi 3 is, well 1 by root 2 is there of course, alpha 1 beta 2 plus beta 1 alpha 2 this time. What will it be? I have written, whatever it is, it will be h, it will be minus 3. Suddenly I got distracted, h is okay. What will the first term be? Ix1, Ix1 is same thing, actually I should not have erased, I should have just changed the signs. But anyway I have erased now, cannot unerase, so just bear with me and tell me what the answers will be. Ix1, Ix1 operating on alpha 1 beta 2, yeah, alpha 1 beta 2 you will get beta 1 alpha 2, right? Plus or minus, beta 1 alpha 2. Then Ix1, Ix2 operating on beta 1 alpha 2, what will you get? Plus alpha 1 beta 2, right? Make a mistake, no, right? Next one what is it? Plus alpha 1 beta 2 or beta 1 alpha 2? Beta 1 alpha 2. Then Iy1, Iy2 operating on beta 1 alpha 2, what is it? Alpha 1 beta 2. Then let us do the last two, Iy1, Iy2 operating on alpha 1 beta 2, minus alpha 1 beta 2 and Iy1, Iy2 operating on beta 1 alpha 2, minus beta 1 alpha 2. What do you have now? What do you have now? So first of all this is plus, this is HJAA divided by 4, right? That is phi 3, right? So first order correction to the third level is HJAA divided by 4. So this is the energy, HJAA divided by 4, simple math but it is just that you have to do it. Now let me erase everything and draw the picture. What happened to this one? This got destabilized by an amount HJAA divided by 4, right? What happened to this? It was destabilized by the same amount HJAA divided by 4. What happened here? Phi 2 and phi 3 were degenerate, right? If you did not consider coupling, the energies were zero. Now phi 2 is stabilized and phi 3 is destabilized. Destabilization is by same amount, HJAA divided by 4. Stabilization is by oh man. Now I have parallaxed. Stabilization here is by HJAA divided by 4. So these are the four levels. Looking at this, we might think that we should still have splitting but let us not forget something. Alpha alpha, beta beta, alpha beta plus beta alpha, right? And this one is alpha beta minus beta alpha. Have we encountered these wave functions earlier? In electronic spectroscopy, yeah? So alpha beta minus beta alpha is unique, right? And the other three form a group. What is that group of alpha alpha, beta beta and alpha beta plus beta alpha? What is that called? Triplet. And what about alpha beta minus beta alpha singlet? And we have studied spin selection rule. In fact, we derived part of it. What is spin selection rule? You cannot have a singlet to triplet, triplet to singlet transition. So this transition is forbidden, okay? Phi 1 to phi 2 or phi 2 to phi 3 or phi 3, not phi 3, phi 2 to phi 4, these are all spin forbidden transitions, okay? And this is what we have learned. What about phi 1 to phi 4? Is phi 1 to phi 4 allowed? Phi 1 is alpha alpha, phi 4 is beta beta. Both are triplets. Are they allowed? Is that allowed? Why not? One photon rule. One photon rule, right? Both have to be flipped. That is not allowed. This is also forbidden by one photon rule. What are we left with? Which are the transitions that are allowed? 1 to 2 is not allowed. 1 to 3 is allowed. I have drawn this wrongly, right? This is also destabilized, sorry. So 1 to 3 is allowed? 2 to 3 allowed? No. 3 to 4 is allowed? What is the energy of this transition? You have this, right? This is E1 where this is minus. I am saying E1 to E2 is allowed. Sorry, E1 to E3 is allowed, right? What is the energy difference between E1 and E3? We have all the correct way, yeah? Sorry? What is the energy difference between E1 and E3? Sorry? H nu dot? H nu 0? Multiplied by 1 minus sigma A, and that's it. There's no signature of coupling, right? So H nu 0 into 1 minus sigma A is the energy gap that you expect in the unperturbed system, right? So what will be the frequency of transition here? Nu A. And what about 3 to 4? What about 3 to 4? What is E4 minus E3? Same thing, HJA by 4, HJA by 4 will cancel, and you will be left with H nu 0 multiplied by 1 minus sigma A. If I write it in terms of frequency of transition, again it will be nu A which is nu 0 into 1 minus sigma A. So what we learn is that it's not as if there is no coupling. Coupling is very much there. It is just that this additional spin forbiddenness comes in for A2 systems because of the indistinguishability of the protons, and that is why the number of allowable transitions goes down. The only transitions that are allowed are between two levels both of which have been destabilized to an equal extent, right? From here destabilization is by HJA by 4, from here also destabilization is by HJA by 4. So it is as if the two levels have just moved together, okay? Same is true for this and this, phi 3 and phi 4. The two levels have been destabilized by an equal amount. That is why you do not see the signature of coupling in the spectrum. It does not mean that coupling is not there, coupling is there.  You have just done some mathematical wizardry and you are saying coupling is there. The situation is equally explainable in terms of this diagram. Even if I do not invoke coupling, I get the right picture, right? So how do I know? How do I know that coupling is even required in this scenario? Well, we know it because we have only discussed the two extremes, right? Yesterday we discussed AX. AX means sigma A and sigma X are very far apart from each other. Today we have discussed A2. That means the sigma's are exactly the same. What perturbation theory cannot do is discuss situations of AB where sigma A and sigma B are not very far apart from each other. For that you have to use the variation method which you are not going to do in this course this time. But when you do a variation treatment, you see that when you go to AB, the situation is somewhat like this. So we are saying that for AX, this is a situation, right? Two lines for A, two lines for X. For A2, situation is this. You have one resonance. For AB, the spectrum that you get is somewhat like this. These two doublets move closer together and the ones inside gain intensity. The ones outside lose intensity. These are called second-order spectra. When sigma A minus sigma X is sufficiently large, much larger than the coupling constant J, then you get what you got called first-order spectra. We have discussed first-order spectra so far. We call it first-order spectra because you can explain those spectra using first-order perturbation theory. You call this second-order spectra because you have to go to higher-order perturbation theory if not a different level of theory altogether if you want to explain this kind of spectra. So you can imagine like this in the hypothetical situation where let us say you have a control over the sigmas. You start with the situation where the two sigmas are very different. You get doublets. Then by some magic, if you keep on decreasing the difference between the sigmas, the spectra start moving closer together, the inner ones become stronger, outer ones become weaker and finally the merge, the outer ones are vanished, the inner ones merge together to give you one line. Of course this is only a very qualitative hand-waving way of explaining the scenario. The correct way of understanding it is by using variation method which can take you all the way from A2 to AX. Variation method is also discussed in Macquarie and Simon. It is not in the syllabus this year but you are welcome to read it. It's not very difficult. You can understand if you read it yourself.


Boomer on and the day's guess we've got a magical and the McLaren and how are we gonna very well James? Thanks for having me. Thanks for being on here mate. Obviously ex footballer. Yeah, but you're a poster But to compare to some people man people look at your careers a success when the Scottish Cup with the D-90 Scotland Caps Scotland under 16 World Cup final Score apparently the only guy Well, there's only three years. I think we scored the final in the World Cup final at the Scotty so It was a good start to the career. The rest of it. I just don't know if I hung my boots up after that So Cassie won't go in. Yep. Right go back to the start mate. So grown-up Cassie won't go. How was it? Ah, it was It was an experience. No, I loved it. Listen, I loved it. Um, there's always plenty of day. Um as I say there was Loads of football pitches in a bit Casimo.  Um As I say, it's Let's go to reputation. Uh, but listen, it's like anything if you're fair replacing, you know, everybody It's it was fine, you know, because I could play football The boys kind of looked after me the older boys and stuff. Um, but no, it was Listen, there was there was plenty of ups and downs. Um, growing up In the late 70s early 80s, it was a it was a bit of a madness, if I'm being honest. Um I say that you would come in and you know Kick to Arsue to Glasgow, kick to Arsue to Scotland, but particularly Glasgow at the time and um a lot of poverty, a lot unemployment and a lot of crime, but to me it was normal. Um If that's what you're used to, that's what you're used to, you know, so, um, I don't It's just a shelf that you'd written That machine You know yourself you're dropping the madness as it becomes you man. It just becomes a norm, you know, I mean You've you seen you see things Probably on the on the normal, you know But it become normalized because you see them not much violence and things like alcohol and and all that So it just becomes a norm here. Um That was that was me growing up When did you realize you had a talent and a gift at right?   Ah, they were a lot older. Definitely. Um, I listen it was for a young age Listen, I probably wasn't a different thing in baseball, you know, I wanted to be a everybody He wanted to be a professional footballer, but for a young age I was I knew it was good, you know, I always played a couple of a couple of years up. Um my first team is the team for Casmo Clyde Boys Club about Mrs. Craig, Mr. Craig took them and they were great people They just wanted to get to beans it but he's after stating give them something positive. Um, so I say I started playing about seven like Um, an organized football about seven before that was always I was always kicking a ball, but you know always You just after where I went at the ball um And that's what people don't see, you know, they think you just get to 16 and sign professional forms, you know, there's There's a lot of work isn't there before that, you know to get to to get to the level where you're playing with Scotland You're getting picked for Scotland under under 16s. Um, and that was What an experience that was. Who's the manager? Craig Brown is the manager and Royce Murphy, but that that full year, I mean Obviously they knew the World Cup was coming to Scotland. So they were putting a lot on it. Um A lot on it in the team. They wanted the team to be prepared and obviously know let the the country down, you know, so um That year, I mean, it was a big year school wise for a lot of boys. No for me. Um, but Because a lot of them are sitting exams and stuff like that, you know, so we've been maybe been Switzerland and I mean, we were away all the time that year. We were um, we went to Switzerland in Denmark and We've got two tournaments, as I say, so we're just getting They were preparing us properly for For the World Cup. Um, and then when it started, well, I was Broughy, you know, Perley came for the opening ceremony. Do you meet him? Hi. So, um, go to shake Perley's horn um For a wee guy, if he cast me, that was amazing. As I say, cast me, cast me, he's five minutes away from Faye Hamden and I think after the first game, I think I'm pretty sure I get the bus up the road, you know, um You're playing the World Cup and then you're walking around and getting to get in the bus up the road Um, but as I say, it was it was some experience. We we drew the first game and then get through the group stages and played Germany In the quarters up at Petodium. We beat him one now and then The semis was a 10 castle There was like 30,000 though. That's probably 30,000, 10,000 looked to it. They had it was here golden generation Portugal's golden generation, the guys like Louis Figo, Ray Costa, all these guys that went on and had unbelievable careers, but we've beaten one now. Um And that was us into the final. Um And again, the final was at Hamden. 60,000 people. I still speak to people to this day that were 1989 and um, as I say, we're two nothing up two nothing up gone well and then They were I remember being in the tunnel looking up at these guys I mean, I've got a photo in my phone.  I mean, I was maybe 15. I'd just turned 16 actually No pubes yet No, there's not any way, man.  Um, and we're two nothing up then physically they were stronger, you know, so back to 28, 20 penalties and I think I was the first one. I wasn't the first one out to take my penalty. That was the first one that says I'll take one. Um, as I say, that's I've practiced for years, you know, and even as a wee guy, we used to get any hand during the summer and The gates would be open so we would sneak in and we'd go and run a bit of partner or that Um, so I'd always I'd always dreamed about playing at Hamden and um, and today that's 16 year old and um, I can't remember my mom and dad with her. Um Then I looked up when it went to penalties and I says, I'm taking the third one and I've seen my mother Reading their huns. Um But as I say, that's Listen, you're playing the World Cup for you know, that's what playing football is all about for me, you know They they big they big moments, you know having That's what you've practiced or eight years for that's what I did, you know I mean, I had to a million penalties before then, you know, me and my brother used to go to the Uh, out of the school across from us and we'd take penalties and that's and I and it was always this is This is the World Cup final.  So um, as I say, I rehearsed that umpteen times and Yeah, I'm glad to see that scored. I put a keeper around me. Um And then after that was as I say, it was back up the road to Casmo. I mean, um back to reality Me and, um, that's a great story. Me and Gary Bowling, um, But it was a boy from the day, please, it was a boy from the day right at the time, but we were a parlay I said, so, so after that we were going, we were going to a party, one of the boys um Steiden Kirk and Tilly, my guy, the convo, um, and he was having a party that night So I'm saying to Gary, Gary Bowling, just come back to mine so we'll get changed and then we'll head out to a party So we've got out of the road Oh, my family's in a mad Casmo house, my granny's, my granda's and all that. It's a rare on the drink, not a thing um and I've So I've, we've had a couple of drinks and I'm saying to Gary Bowling, right, we need to go and get a carry out So he's looking at me So there's a pub around the corner. Um, it's our way now, but it was, it was some pub that was a mad to us. Um But I'm only 16 year old, so we're walking around and he's like, all right, get a carry out and I'm saying, aye, aye So I've just walked right into the pub. He's looking at me as if, what are you doing? Walked right into One of the other officers says, how are you doing? She's like, uh, brilliant Andy.  I was drinking about 12, 13 But he's about a wee bit older, so as I say, I was, that's what everybody done Right, I pass you, do you want it? I see pure hours Pure pressure around, I was, I was, I was like, why do you need me to drink all day in it? You know, I mean, I was, I was a willing participant for a day What?   All the brothers getting through at the house at 12 o'clock at night fighting And they were fighting each other, and the brothers fighting, and that was, that was, that was, that was the way it was, it was, that was the way it was Wake up the morning, you get your murals and saucies, get your papers and I used to go out with my granny since she always had a big pot of soup, always had a big pot of soup So my granny snagged right across the park here, so I remember even when I played, you know, it was Obviously when I got in at the first team night in the night, I would get her there, just walk across the And get a big plate of soup, you know, you never even go to a plate, you just had a big ladle, you know what I mean?  But as I say, I fitted right in it, you know, you probably would change it Grown up there, man No, that's nice Part of the effort, man It made me work more, you know, it gave me a lot of lessons Um, and I grew up with good people doing about me People that maybe drank drugs, maybe got a grip on them later on in life, but they were good people, you know, and Life wasn't, wasn't he, maybe as kind to them as other people, you know, and maybe end up with addictions or Just maybe never a good start in life, you know what I mean?  The thing is, you're going up against a country, aren't you? Because they've obviously got passports and all that sort of being dropped and that kind of thing So, I must have been, I must have been, and FIFA has done no hardly going up against a country You see it about like Nigerians and Cameroons, they play under 18s, but they're 24, 25 That has come out in the past I think there's something, there's something to do, because There's been so many boys that's come out here saying Nigeria and all that and Telling you they're 15, 16 and I don't know, they're 21, 22 But how do you prove it then? It's all the later on, once you get there, mate, they're 28, they're really 35 Can they run, you know what I mean? Right, so, but I think they do something, it's like a bone check or something, aren't they? They can, they can do something They can, they can, I think clubs do that now Because I think they've been getting stung a lot Who was all the boys at Scotland, Andy, that you played way to there?  I signed when I, probably about 13 I think I signed when I was about 12, actually I signed a schoolboy for, when I was about eight times There was a lot of clubs that I signed me Rangers that I signed me as well But, I went to a certain school at that time You're allowed Well, Rangers wanted to sign me, they were changing it all But, going to school in Casemont I can try to outrun 500 people every time I was quite, I wasn't, I've been going back So, ah, listen, my dad was a big Rangers fan So, listen, I did, I don't, I've never been caught up No, not half of my farm myself finds an awful Ranger So, I find that that's a part of Glasgow that I don't really like, you know There's some of the, there's some of that crap, you know And because we're all, and everybody gets on it at the best of times, isn't it?   But you know everything, don't you?  Oh, aye Partying in that before the United days Were you ever pissed before a game? No, no, no, no I had never, I wouldn't have drank that Friday night I mean, if some of the stories I've heard of it, we've been able to be true I would never have made it I would never have been on a photo party Anyway, you know, I mean Taxi drivers are brilliant, aren't they? You know that Me and Charlie, I mean, some of the stories that have been told about us to I mean, we wouldn't have been No, so That's the worst one, you've heard I've heard of, I've been crawling up Casemault driving a Friday night for a game and things like that Oh, that's push, you know I mean, I was standing there, you know I mean And I never crawled anywhere, you know I was I was taking other stuff to so I wasn't crawling about, you know So, aye, but as I say If I'd been up in the United, I was partying I was I would be going out now I would come home on a Friday night or a Saturday, depending on whether you've been on the reserves or the first day or that And at that point, 89, 90 the rave seam can have exploded and the glass would have done it So, me and my pals were gone, you know My pals were working, organising some of them and things like that So, I would come home and my pals would be going out What do you do, sit in the house?


I'm gonna start with this one. This is from long for I think long for let me just double check Yeah, long long for at long for I don't know what his actual trainer name is but he's Japanese player He posted this on Twitter. I popped up on my feed So I thought it's a nice team for us interesting for us to start off with blast toys It's always been allowed in series six and it's a G max as well It's got that crazy G max ability with its residual damage. We've not seen much of it Our series six. So I thought this would be nice. It's got surf etched in there as well So we'll give this a go Jamuzu playing wheezing Galarian form wheezing these green mustache Krugadal Barascuda Tang Roth Ralladon and Intelion Now what are we gonna do here? It's done monotone. It is scoff. So we can do some damage And we get rid of something and we make use of it in this match I mean it we may be able to I think blasto's isn't bad And comfy course comfy. I prefer comfy to have the I think we need. Oh, do we want do we want surf etched or do we want Draco's alt? Hmm? What am I gonna max probably blasto's so let's go this and let's go this Yeah, let's go that and that let's try it. Let's try it skipper. How are you doing? This is a good name. How are you both doing? Hope you're both well Hope you had a good day ready for some games tonight if you've got rental teams like I'll say to everyone Chuck them over and we will feature them this evening. Can I have a good old? Sloggered out on rental teams tonight and you guys can help me get back to masterball ranked here because it Seasons reset. We're in a new we're in a new month. So the rankings have reset I'm hoping what we can do here is and Well, we can fake something out. We could just go Is it a waste to go? I mean we could fake out and just what's not gonna max though I don't think in I think the intelligent max is here. That's the thing I don't know if we'll be able to get a trick room off. That's the problem Let's fake up barracuda and go for a trick room I'm hoping we can get the trick room off if we can that'd be a mate. Oh, it might happen. It might happen Say, how are you doing coming at the most exciting moment of this all for me? Unique banana I left my last class early to watch you dude I hope you're not missing anything too important But I appreciate it and I hope we'll make it worthwhile for you tonight and with plays like this a Guarantee it's gonna be a lot of fun tonight. I remember that there is there you can cash in some of those goodies as well tonight And I think what we could do is just water spout and gig Let's let's start this let's start the hydro canning get this weakness policy prox. Let's do this Well, how are you doing mate? I hope you're well only team I have in game is the team I used in plays cup Dude It's not gonna work tonight. It's not gonna work. What about you and tell you on team? I saw a tweet I didn't really get a chance to read it today Flash by and then something came up So I had to put my phone down but something about a team that bars is using. Is that your team or is it not? I don't know Okay, so there's the gig of terrain There's the weakness policy computer kids. How are you doing? Hope you guys are all well Hope you've had a great day and I'm looking forward to Zika and we will say bye to mr hukadal Before we can do too much damage to us Okay, well, that's worn down free to go. Let's see if Blastoise can do this flip turn Okay, well, I do like this move. I do like that move. It's cool move Oh, you can play that team. It's on my other card. I'll shoot the card Nice. I built the team and bars made a few tweaks. Nice. Okay, dude. That sounds good. That sounds great. Sounds great Okay, well, we got one team. We got one team tonight. Yeah There's well saying look at well. He's like I'm keeping this keeping this for bears Barry Barry Anderson only team I'm joking. I'm joking. Well, I'm joking. Um, okay Well, I think we could start gig of draining the intelligent for sure If we want or we could help in hand I think we'll probably be able to take the Duralid on with a max hail storm to be honest Intellions probably gonna max maybe Duralid on though It probably is the Duralid on there's a beast ball coming out Do we get max Duralid? If not, if it's the salt best new way Gonna end a little legend tournament with Marsh shadows swagger Grim snarl. That's a nice idea, dude My shadow is very cool Pokemon. I do like it. It's definitely on that top tier list of either the Pokemon that are allowed Comfy so good. I do love Comfy That's your cool Pokemon But such a cool design as well, right? Let's see. Can we do this if we get rid of this thing? It's gonna be a very quick game for us. Oh No, it's it's it's a salt best, but the residual damage with the hail and things will start stacking up They're gonna probably max lightning us. Yeah I think that big thing is to try and get rid of our Comfy really would make more sense to do that, but we'll see what happens this next turn Snipeshot, I don't know if we're gonna be able to take this but it would allow us to get oh We can take that like a champ. Okay Comfy is way stronger than what I thought it was Okay, everything taking a bit of residual damage Johnny can't stay today Lee stuff came up and I have a great stream Hey, thanks so much for hopping by and wishing us all the best Johnny. Have a great evening. Whatever you're up to mate I hope you have a fantastic time and Could we max strike on our last turn just to lower the speed so when the trick room ends? What have we got in the back? Got now what we got in the back. That's what we need to discover. We've got surfetched Hmm. I don't think we're gonna be out speeding anything still It might be worth it might be worth just going for it. Anyway And go for Yeah, we'll go for Yeah, max strike is good and we'll go for a helping hand there and that Hey Ken Ken Ken's how you doing mate and quiver quiver dancer. Thank you so much for the follow. I'm doing good, dude I'm doing really good. Thanks for asking. Hope you're doing well mate. Hope you're doing well Well, we're just kicking off dude. So hopefully we can open with a win. That would be very good for us if we can I Think the Duraladon's gonna steal spike Comfy this is our last turn of our max with Belastos, but we have okay They're not they're not getting rid of the they're not getting rid of the comfy going after the blasto is blastos has done its work Kessel 76. Thank you so much for the follow. Thanks for joining us tonight. I hope you enjoy the stream of this all friends I'm not crafty leave first off. Thanks for the advice on discord I got a shiny G max alchemy nice, dude. That is so cool It's one of the nicer G max shinies as well. So I'm really pleased that worked out for you, dude And anytime no problem. I'm always happy to help I think well, we can get rid let's let's bring in Let's bring in surf fetch to see what you can do. I mean we could be it Okay, are we well are we even in trick room? I need to be paying we are we are in trick room Okay, we've blocked this because they have to protect here if they don't then they're done And we'll just giga drain and that will that will do it so fetch this here is arrived Kessel and trying to make a size band team with alexa any suggestions, okay for which series, dude That would make a lot of difference if we're going for series seven. There's a lot more options there if we're doing it in I see we six obviously we're a little bit more restricted because we've got the band Pokemon So yeah, just hit us up with which format and then we can we can kind of go from there The max strike is totally screwed us. Oh Okay, that's not good that really isn't good but We might be all right. We got two Pokemon left to do some stuff with so it's okay The first time we reached top 100 on the ladder, dude, I am surprised by that. I'm very surprised by that Honestly, that surprises me massively actually You should be in top 100 all all the time. Oh my bar skewed is still kicking around Forgot about bar skewed it. Okay. Hmm. The Ralladon now Gonna start chucking out. Okay. Well, hopefully a giga drain. Can a giga drain? I don't know if a giga drain is gonna be enough to get our scooter But do we just do we just dazzle I think Yeah, we'll just dazzle and we'll go giga drain. I can't afford to go trick room. I can't believe I've let this slip So I so I I think mmm. Do we get the bar skew? I'm not sure if we get the bar skew Do you know? Maybe would have been better protecting hats, but then if we protect hat and then they just double into comfy Anyway, then we're left That's very close Very close Lip turn is that all we're doing? Okay. That's fine flash cannon into Comfy and we got the bb reburied.  They have to be this zoom Okay, we've got urshifu comfy talent flame a moongus toxer is deep and drake of ish Well, well, well, can we I think we can I think we can go blast us again You have to be very careful around the moongus though. The moongus worries me slightly A lot actually we can bring a hat though. So we don't need to be And probably It's a fetched raker's alt or dohmanitan I think because it's scoffed and I feel like the other three can deal with everything we'll go dohmanitan We'll bring that to a game and beb them.  I I'm looking forward to seeing the kabut ops. I know you've mentioned it before but yes Kabut ops all the fossils are back as well in tundra Which is it kind of gets overlooked a little bit We're gonna have aerodactyl gonna have all the fossils which is really exciting because some of those fossil pokemon Extremely good. Okay. So Um, the toxicity is a little bit of a pain for both blastoise and confie um I don't know if we're going to be able to get a trick room up here because I think we're going to get taunted um But do they max turn one that's the thing. I don't know if they do We could try we could try I feel like we might get caught out a little bit though Okay Well, let's go for it. Let's just fake out. Let's hope we don't see any max no maxing It's definitely not what we want to see Okay Perfect What is this? How are we getting away with this? How are we getting away with this? This is like the the best case scenario every time. I love this I'll be back. How are you doing? I hope you're well They give aerodactyl dragon dance No way Aerodactyl gets dragon dance. That's nuts. Picatrina. How are you doing? Is there a way to request rental teams? If for you to if you want me to play your rental team if you've got one if that's what you suggest You can just post it in the chat right now and I will grab it and we'll play that tonight Um, if you're referring to any of the teams that we're featuring if you want the rental teams Then I can show you those as well. So uh, just whichever whichever way works best for you Okay, so we are gonna max Blastoise and go after the toxterity here because we need to get rid of it. Otherwise, it's going to cause us all sorts of problems Awesome get the card. That sounds great. So thank you very much as well for providing them And thanks to anyone that provides a rental team for tonight. It's always great playing your teams And laroct 93 hope you're doing great. I am doing great my friend. I hope you're doing well as well Thanks for the stream. Here's a coven at weakness policy team. I'd love if you could take a spin I would actually love to do that. So thank you so much. We've got our first one. So that's great Oh, no Toxterity is just g maxed. This is not going as planned Okay, well we should Hopefully be able to take an attack from toxterity. I'm hoping I mean the hydro cannon is gonna do a bunch of damage to it I don't know if it's gonna be enough to knock it out. I really don't but toxterity isn't the most bulky of pokemons So We might be able to take it down if we take it down now We either see one of two things a rage quit or a battle cancel We'll see we'll soon find out But if we don't take it down, we're in trouble What? No way. It's actually slower than blastoise. Okay That's bad. It's really bad Okay, that's really bad Okay, now we're both. Okay, blastoise is poisoned. Confuse paralyzed I thought blastoise would be minimum speed. I wasn't prepared for this Picatrina awesome This is my ic team I built around Pichu nice. Okay, this sounds cool. Okay. Thank you so much friends It's at the Pichu team the Pichu team. I feel like I need to be aware of this Pichu team This sounds a lot of fun. Thank you so much for that. I look forward to So after this, I'll plug in all of the rental teams that we've got so far and then we'll jump on with them I got a very special team as well I'm going to wait for nappy because nappy normally cops on midstream when we're streaming. So he's past us He has past us. We are in trick room. I just need to make 100% sure that we are in trick We are in trick room. Okay, and this ursia foo is probably the dark fighting type one I'm going to I'm going to assume it is I need to go why Check you out. Yes. It's got sucker punch Okay, so we need to go off. Um Actually, yeah, we floral healing. I've last voice and then we go after The ursia foo Because floral healing will go before the sucker punch So we should be all right should be all right There we go. Okay. That's fine I just realized we don't have draining kiss and then it had this little panic on there and I was like, oh, no Okay, so there's a sucker punch. Yep. Okay, so the floral healing allows us to take that pretty comfortably We are going to be able to get rid of the ursia foo Yep, okay. I think it was bounded as well Yeah, so that's two down We've got another brave bird coming out from this talon It's going after that confi still. Okay. Well, this is all right because another Couple of those and some brave bird recoil will put that down the range So we've got one pokemon to deal with no g max left unique banana with the team as well This is a trick room team. Thank you so much my friend. Okay Mr. Fish coming in mr. Fish is about to eat Fat old Max hail storm And then the hail of residual damage should take down Flam bazaar bazaar blame bazaar And pico trainer I went 10 6 and it with the ic but I had a tug of kiss over for you can see I didn't feel like playing or 45 games.  It's such a slog sometimes, isn't it? Look forward to seeing the team and playing it though. So thank you so much snowman One point we've got another team Okay, perfect. Thank you so much right This is great. Thank you so much friends for all these teams Working out. It's working out perfectly this evening. This is gonna be a lot of fun. I'm looking forward to playing all of these This team that I'm playing now I will give you the rental for because it's um as a Long long for I think is his username Hopefully that's not coming up on the screen now. It's not. Uh, yeah um at long Fop long fop. I don't know what his actual Real name is but his japanese player It popped up on my timeline earlier with this team and I was like, oh, I need to play this team. This team looks this team looks awesome um so Did we not actually manage to take down the um The drake of ish we didn't wow I'm surprised that hung on Okay, so we're in a decent spot now. We're still in trick room. I think the last turn so we can bring in Are we in the last turn trick room? Even if not, I mean confi's gonna be able to deal with vista fish With a giga drain And then Let's just double check. Yeah last turn. So that's good. Um, yeah Yeah, we'll go for a giga drain and a dazzling gloom and that should take us to two wins to kick us off with It's a copycat trick room team unique banana. That sounds cool. I like the copycat stuff. It's always good Um There's something I brought like that just reminds me copycat. There's a oh, wow. It's got protect as well. Huh, okay um Yeah, there's a team that I I saw a while ago with octovish and a zoomerill and a zoomerill copycatting the The fishes rend it was nasty. It was nasty. Yeah, and ever since I saw I was like I need to try and get that combo working in a team But I've just never Got around to it like the list with things to try in series six is crazy Like I know a lot of people say it's the same sort of thing and like top tier Teams are kind of the same cause and stuff like that But there is still a lot of scope to try different pokemon out, you know Um, and a lot of different strategies are way more viable because you haven't got those top tier kind of Like suppress and everything else like they normally do um So We'll end this one up. Here we go Uh, I by back I've been running into a lot of scoff chandelier To one shot my durant. Yeah, it makes a lot of sense. Like scoffs shandy is really really good It's probably one of the best counters to durant Honestly, when I was theorizing the very start of the series as like like scoff shandy kind of comes down As one of the best pokemon in general to that because you're seeing a lot of durant Especially paired with goth for town You've got that option to switch shandy out because of its ghost typing as well So it gives you a lot of flexibility. You can kind of optionally imprison trick room if you want So it plays a lot of like roles in one pokemon. So I can do a lot of things um Yeah, choice band there. Okay, so


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Luca Health works in collaboration with patients doctors to provide specialized and same-day surgical care. The Luca Health Medical Specialized Center offers specialty and same-day surgical surgery and occurs to U.S. standards of safety, patient care and doctor-patient confidentiality. It is situated in the center of Accra. The doctors and nurses at the Luca Health Medical Specialty Center provide patient-centered care in crucial moments for our patients by utilizing the most recent innovations in medical interventions and taking use of our telemedicine partnership with the New York University School of Medicine. Our clinical and nursing team is dedicated to providing patients in Ghana with the same high-quality specialist treatment, same-day surgical interventions and cutting-edge diagnostics that they may find in the United States, the United Kingdom and South Africa. In West Africa, we at Luca Health are dedicated to making sure patients get the treatment their doctors recommend without having to wait or travel elsewhere. Top surgeons and doctors from the U.S., E.U. and Ghana are drawn to Luca Health's world-class medical center, which combines their specialized knowledge with cutting-edge medical technology. We are able to provide some of the greatest medical treatment in Africa thanks to this. Modern techniques, such as minimally invasive surgery, are used at our advanced medical center with little incisions. Our specialists provide a secure, welcoming environment where you can receive treatment for your symptoms and ailments with less discomfort and a quicker recovery. Our procedures frequently require less time and allow for a quicker recovery. Our specialists will help you feel better using advanced techniques and equipment, which results in less discomfort and a speedy recovery. Appointments are currently available. Changing medical care in Ghana. According to Dr. Armstead, 25 of the world's diseases affect 11% of the population in Africa. That refers to people getting chronic illnesses like cancer, diabetes and hypertension. Whether it's a surgical specialization or a medical specialty, he argues, these astounding figures show the need for treatment. He argues, these astounding figures show the need for filling the exceptional specialized gap. Therefore, in order to receive the necessary medical attention, they had to leave West Africa. They can now receive that care closer to home. As a center of excellence owned and operated by the United States, we will supply these types of solutions through a high-quality patient-centric paradigm, not only to Ghana, but to the rest of West Africa. Instead of people seeking care in India, the UK or the US, we will become the preferred referral location. Why Ghana? Prior to joining UnitedHealthcare, Dr. Armstead worked briefly for the government during the Clinton administration and was on the lookout for private equity options. Here comes Cheryl Mills, CEO of the sub-Saharan African-based investment company Black Ivy Group. The former US State Department Chief of Staff, who identified a great potential to invest in Africa. But which of Africa's more than 50 nations would be the best choice? The country's GDP growth trajectory, the state of its middle class, the stability of its democracy and the history of its support for private investment were all factors to consider when choosing where to invest. As a result, the search was limited to Ghana, Tanzania and Kenya in West Africa and East Africa, respectively. Given that Black Ivy had experience working in East Africa, it made appropriate to select a dynamic metropolis with a population of more than 4 million as the hub of Luca Health in West Africa. In the United States, creating a new medical facility only needs determining the demand and needing it. But in developing nations, there are many more obstacles to overcome, increasing the initial risk. Investors needed to be persuaded that Dr. Armstead could construct the hospitals, entice physicians to practice there and encourage patients to seek treatment. Because that runs counter to how you would expand in the United States, he claims it will be difficult to persuade investors of that. After the investment was confirmed, he had to deal with Ghana's peculiarities. Understanding that you must actually be here, live here, understand and accept how they do things and possess a certain degree of humility is necessary. For instance, he claims that just because something is written in a regulation doesn't necessarily mean it operates in that way. He claims that overcoming this major mental barrier requires being in Africa rather than overseas. Thank you for watching this video to the end. With this new hospital, Ghanaians and Africans will have to stay back home and receive top medical care. If you are new to Africa Reloaded, please take a few seconds to like this video and subscribe. Also, do not forget to turn on the notification bell to get notified when we upload a new video.


Good morning. Good morning everybody Russell more coming to you live the channel is dedicated to financial literacy and We are dedicated. We are dedicated to financial literacy. Amen. So, um Good morning, everyone. It's Monday morning 9 30 Pacific time. I'm here on the West Coast Camarillo, California just about an hour away from Los Angeles LA where the LA Lakers live in the Los Angeles ramps By the way three and oh give it up for the ramps. We beat hey, Brady. Sorry, buddy. We got you. We got you Brady We got you anyway. Good morning, everybody. How you doing? Um, First of all, I want to do a quick update of what's happening with the stock market the stock market is Kind of choppy today, it's just kind of undecisive The S&P 500 was about at age about 20 minutes the last 20 minutes when I checked it was about Eight points under eight points in the red the Dow 147 points up up the Dow and then the NASDAQ was a hundred points down So S&P 500 eight points down NASDAQ a hundred points down and the Dow was 147 to 148 points up. We'll see how it ends. Okay, keep an eye on the market all you traders out there and investors now this channel is really about Financial literacy teaching people about how to be financially litter literate and So we go over various different things We go over housing at the last few episodes. I've been talking about ADU's accessory dwelling units and how valuable they are especially particularly in Los Angeles right now and how so Many African-Americans do not know not just African-Americans But particularly the black and the brown a lot of them do not know anything about ADU's and the power of having an ADU If you own property in Cal in Los Angeles because why the inventory is so low homelessness is up We need housing we need housing and so the the state of California is actually past several assembly bills And I went over in any other episode so I'm not gonna go over it today But they went they have passed a lot of things that have made it first of all cheaper to build an ADU On your property They've allowed they've removed some of the stipulations and all the resistance and it's a lot of things that they've done Okay, I would I would encourage you I would encourage you Google ADU in California. Okay, so So we talk about budgeting we talking about getting out of debt We're talking about credits your credit getting your credit right getting your credit together You know a lot of people have all these different hacks on how to To improve your credit score, you know how you want to prove your credit score Hey them Hey, the people you owe. Oh No man, but love that's all you should owe them is love Pay them Your credit score will go up Get rid of all that debt begin to say no to McDonald's And your Netflix subscription take that money and put it on the debt Put it on a credit card debt Say no to some of your luxuries Until You get out of debt and then you can splurge a little bit. I'm not against Netflix.  I get it But not at the expense of being in debt Say no to Starbucks for about six months and take that five hundred dollars that you've been spending monthly on Starbucks and Take that and put it on a credit card that you owe or that home Depot card lows That JC penny card whatever card Begin to look at your debt and attack it attack your debt and If you attack your debt Great things awaits your future You'll have the freedom to do so much more when your credit is much better You know, I was looking at our credit score me and my wife and I'm not bragging this is not bragging It's taken hard work a lot of discipline. We've had to say no to a lot of things Including going on vacation for the next the last two years We've had to say no I was looking at my wife's credit score is around 780 790 and I'm at 75 775 We're right behind each other close to depending on which Credit bureau you're looking at one of my credit bureaus from 790 But our goal by the end of this year is just be at 800 and there and stay there Okay, so Make that your goal say tell yourself look I want to be here at a certain place as far as my credit score is concerned and Then begin to make a plan on how you're gonna get there But I would say that about credit score.  Well, they didn't settle with you when they loaned you the money They didn't say well, we'll give you a partial of what you're asking for it wouldn't have met your need I'm just saying yeah, I'm just saying they did not give you a settlement Do the right thing one thing that I push and this is what I do is well This is what I push or anybody I coach and as far as finances is integrity So I don't tell them to get a settlement now if you have to do that, okay If you absolutely have to but keep in mind they did not give you a settlement when they landed you the money They gave you what you asked for if for what you qualified for okay. All right Let me get off my rant. All right. Let me do today I just want to talk about one quick thing and one of the things that I'm doing with my channel is that I am I'm not gonna be long. These segments are not gonna be long I know that you're busy. I know that you don't have time to just sit there and listen to people just gravel You know, it's got to be something that's gonna benefit you And so one of the and one of the things with this channel I deal with financial literacy But I talk about the stock market I talk about stocks, but it's basically for newbies New investors those that are new to the stock market particularly of course. This is not for institutional institutional Investors this is not for the mutual fund guys. This is not for the hedge funds. It's no they're not gonna be looking at There's something like this This is for the retail investor. You're brand new to the market. You don't know what you're doing You lose money one week and make money the next but you haven't been making any gains Here's what I want to talk about Why am I not making gains in the stock market? I'm new and I'm not making any gains Number one I say this all the time Anybody that knows me and there's a and text out my channel. This is what I say all the time if you do not Learn you will not earn. I'm gonna say that again. I was I was mixed to get up in my mind if you do not learn you will not earn number one Learn as much as you can Read books About stock market Read about charts in the value of knowing charts Read about trends read about technical and of being you know technical analyzing read about fundamental analyzing which is what I push a lot Because it because it means that it means that Fundamentals if a company is fundamentally sound they have a good good good good leadership and executive team Excuse me the PE ratio is strong The profit margin strong Revenue strong cash flow strong Are they growing do they have a competitive edge? Those are fundamentals Now I'm not saying that technical analyzing is not as bad. In fact, I think you should learn both But the first thing you want to do is Is if you don't learn you will not earn so you got to learn Okay, now it's not just about learning and getting a bunch of information practice number two Get on a platform and there's a lot of most of the platforms will have practice sessions Okay Where you can paper what they call paper trade? It's not real money It's a simulation So get on there and practice because this is one of the values of that is that because you're not trading your real money Your personal money you'll be more free to take risk and that's how you learn the fearful Will be tearful Let me say that again. I said the fearful and investing in the stock market will become tearful So Simulation trading will help you break a lot of your fears now once you get your real money. You still got to attack fear So paper trade Okay Number three get a plan Decide what you want to be number three decide what kind of a trader or investor you want to be I Like to put them into three categories Day trade here's the thing about day trade though usually Because of them there's a day trading rule From the FCC a day trading rule you cannot exceed more than four trades a week and Then if you have those four you got to wait a week Unless you have $25,000 in your account So unless you have $25,000 in your account, you're gonna be limited on their day trading So I never suggest to anybody that's just starting out today trade Unless they have $25,000 and even if you have $25,000 you need to be a little bit more experienced because Decisions you're gonna have to make her a little bit quicker. You're getting in and out of different trades It's gonna require a little bit more. So that's the next Category or the next area is Swing trading Swing trade swing trading is and day trading by the way is Day trading it's you buy that one day and you sell that same day. Okay day trade. That's pretty simple, right? Swing trading is anything from a day and After a day So you buy the stock today you sell it two days from now three weeks a month. That's swing trading and Then there's positional trading or long-term trading Where you buy and you hold it you do you have no intentions on selling it you're looking for gains a perfect example of that is warm Buffett Warm Buffett is probably the greatest of all time Unless you add Benjamin Graham in there who's The intelligent investor that's a great book to read by the way, so long term So you got to choose which one am I I Do all three I grew into that though. I do some day trading. I definitely do swing trading That's mostly me and then fourth. I mean and then lastly I do I have some long-term trading and each of those are in different platforms So my fidelity count is for long term That's more buy and hold positional trading my Robin Hood I have two options and it's a lot of swing trading and day trading and then I have a Ameritrade TD Ameritrade which is mainly Swing trading so my day trading is more in my Robin Hood account Okay day trading and I do some swing trading in that as well as well as options Okay, this is not about options if you're new I know you want to make money Here's the other thing I want to say number four You must deal with your emotion Your emotions what I mean by that you must make a decision that I'm not going to let my emotions rule my trading There will be times When everything in you is going to be telling you screaming at you sell this stock sell this stock and Your feelings because say it's going down and here's what a lot of new traders do the stock starts going down And they're like oh, no, I made a mistake and then they sell it Here's what you have to remember you have not lost any money Just because the stock goes down does not mean you have lost money You lose money when you sell it after it's gone down and Many times let me tell you there's an old saying what goes up must come down what goes down usually goes up at one point It will go back up Her for example MG MGM resorts Pandemic it was at $12 You guys it had sunk down from I think the previous high was $50 something it went down to $12 And I had you know, I people were selling it selling it selling it held it Do you know where it is now? We're talking about a little over a year later a year and a half later 18 months later MGM resorts is at $44 today Just just when the pandemic started it went down to 12 probably I think it was less than that $10 If I let my feelings run me and tell me what to do I would have sold it You buy on the dip That's my next point buy on the dip buy on the dip Wait and buy on the dip load up when catch it when it's on a discount and hold it It'll make money for you People that were disciplined and patient are Making money this year Because the market is not doing this it's not doing what Tesla did. Yeah, I rolled the Tesla wave, too I was on it. I Was on that my little Tesla surfboard and I rolled the wave But that most stocks aren't doing that they'll do this and Upward trend slowly over time and you have to be willing to wait it out You have to be willing to wait it out. Um, this is it. I wanted I told you I was gonna be I gave you five good points Okay You can be a great trader you can be a great investor save your money get out of debt Invest in the stock market and don't forget to get some land or some property at a house get some get some property too so that you're So that your portfolio is diversify Hey, everybody that's doing these channels and putting out content. They do it because they really care At least I hope so. Let me give you a few people that I want to recommend. I Don't recommend a lot of people but on YouTube. I will recommend these three Number one as far as the stock market is concerned Jeremy with financial education Jeremy. That's his name Jeremy financial education YouTube him a lot of knowledge you can tell he's done a lot of research. I Do a lot of research myself, but that's not what kind of channel this is I just want to encourage people and give tidbits Every day I'll just come on and just give and give tidbits I'm doing it once a week right now, but eventually I want to get on on on on my channel every day And just giving people little tips hacks Investing hacks The next guy is meet Kevin Kevin meet Kevin is awesome. He ran for governor actually And I was I was like I was pulling for him even though I voted for Larry elder Because I'm sorry governor Newsom was doing he's still doing a very bad job Sorry He had less we got to be honest black or white no matter what color no matter what didn't no matter where you are from What side of the coin right left? It doesn't matter the man has done a bad job as governor here in our State all right, and then there's Graham Stevens. He's he's excellent too the latter two Me Kevin does deal with stocks a little bit, but I really believe that if you want them as far as the stock market is concerned specifically Jeremy with financial education is I think that one of the best out there. It's not the best He's very very good. All right, so I just want to tell you guys. I love you very much have a wonderful wonderful week Hey, let's keep checking on that market and hey short when you can go up when you can But the key is you cannot time the market. You don't know that you don't know when it's gonna go But be prepared make sure you leverage your risk if you're if you get if you're going long make sure Make sure you're covering yourself and I'm not saying shorting the market We'll talk about that one other day But I'm what I'm saying is make sure you manage your risk as well. We'll talk about that. All right. Have a great day I'm sorry you guys. I know I just be running my mouth, but I love you and I hope the best for you Have a wonderful wonderful week All right


Let's quickly summarize mitochondrias and plastids. Let's start with mitochondrias. They are called the powerhouse of ourselves and they look somewhat like this. You can see that there are two membranes. We have the outer membrane which is usually porous and then there is this inner membrane which is highly folded and the reason it's folded so that there is more surface area but this is the place inside the inner membrane where your digested food, the food that you eat that is converted into energy and that energy is released in the form of ATP and so that ATP is generated inside the mitochondria and that ATP is the energy that your body uses. Everywhere, wherever your body is using energy it's in the form of ATP and this is the reason why mitochondria is called the powerhouse. Without the mitochondria, the food that you eat will not be converted into ATP and you wouldn't have any energy. Mitochondria's are super important. They're found in the cells of both animals and plants. But now let's go to plastids. Plastids are found only in plants and algae. But what exactly are they? Well, they are of different types and they have different functions. Plastids comes in usually you can differentiate into two kinds. You have something called the leukoplasts. These are colorless and you have something called the chromoplasts which have colors and you can see chromostands for colors. Now, leukoplasts are mainly used for storage. Storage of fats, proteins, lipids, basically storage of nutrients. Chromoplasts and on the other hand well their main job is to give colors. So they are responsible for producing a lot of colorful pigments. Now, one specific kind of chromoplast which you might be familiar with is the chloroplast. Chloroplast is the one that has the green pigment. So you kind of see how it is, right? So chromoplasts can be of different pigments and they might have different colors but the one that has the green pigment is what we call the chloroplast. And the reason that's important is because not only is it green but it's also responsible for photosynthesis, right? Chloroplasts are the one that do photosynthesis. And so let's look at its structure now. So again, you can see chloroplasts has two membranes. It has the outer membrane and then there is this inner membrane. And if you go inside the inner membrane you'll find the whole region is filled with some kind of a fluid which we call the stroma. This coin-like structure stacked is not the stroma, okay? Stroma is the fluid that you can't see. It fills up the inner membrane. And then finally, if you go into that coin-like structure you will find molecules of chlorophyll. And it's these chlorophyll that has the color green that has the green pigment. And they're also responsible for trapping the energy of the sunlight and helping us make food via photosynthesis.


Fine, so there is one part of our section in this chapter which talks about force on a current Right, we have learned that a moving charge will experience a force Right, how much is that movie charge experiences a force of magnitude? qv cross b Right now when when I say that current is there, okay Does it mean that charges are moving? Yes or no? Which charge is moving? Positive or negative? Negative charge is moving and positive charge is stationary Alright, so charge is moving So if charge experiences a force Then automatically the wire which has the current will experience a force Isn't it? Now it is difficult to measure the charge That is why one of the reasons charge is not the fundamental unit The current is the fundamental unit Right, current is very easy to measure Okay, emitter or galamometer whatever it is You can measure the current very accurately So for the practical purposes it is easy for us to deal with current And to find out how much force is there on a current So we would ideally like to know the force on a wire that contains a current i Fine So we will try to use this expression itself to derive the force on a straight wire Which has a current i Suppose there is a wire like this Current is i Cross section area is a Number of free charges Current volume is n The length of the wire is l Okay And inside the drift velocity is vd Okay, drift velocity is like that Current will be in opposite direction Because it is electron Can you get this expression of force In terms of all these things vd, a, l and n Okay What else is given is Entire thing is in a magnetic field b That is perpendicular to the rod Going into the plane In terms of a, vd, small n and b and l Get the value of force The hint is The total amount of force experienced by the moving charges Will be the total force on the wire What will be q? q will be what? Here Total charge that is moving inside this wire How much is that? Small n is number of free electrons per unit volume So how much charge is there inside this wire? Number of electrons will be what? n a into l Right So total charge will be what? Number of electron into charge of one electron Getting it Now what will be their velocities? What are their velocities? Not just vd They will have a random velocity As will have a drift velocity Because the random velocity net force gets cancelled off So we do not need to consider the random velocity Only systematic velocity will have a net force Fine So we will ignore the random component We will say that this entire thing is moving with vd So charge q is moving with vd Right And this vd is perpendicular to b So vd cross b is just vd into b Fine So the force becomes what? q which is n a l e Then vd cross with b Like that Which direction the force will be? Tell me vd cross b Which direction? vd is like this Cross b It is downwards So the force is This is electron This downward force would have been on the positive charge On electron it will be opposite Fine This is the force Getting it vd cross b Down on a positive charge It is a negative charge So it will be opposite of that Fine These are electrons Fine Now if I Sir can we use the left hand rule also? Yes sir This is n e a vd l cross b Right Now what is this? Can you recall? I This is i Right But once you represent it as i You cannot have a vector inside i So what you do? You drop the direction from v Down to length You make length as a vector And what is the direction of this length vector? In the direction of current Or opposite direction of the electron velocity Getting it So if I write this as i l cross b I will get the Direction of force Fine The direction of force is in the direction of Length cross product with 93 And length vector is in the direction of current Just check whether you get the upward force Only i cross Sorry l cross b l is like this In the direction of current And b Upwards Fine In order to find the cross product Align your right hand towards the first vector And then fold your hand towards the second vector Thumb is the direction of cross product You cannot do like this Then you have to fold this way You have to do like this and like that So this expression Is what? Force on a conductor Of length l Which is in the magnitude b Till now we have been using this What if the conductor is like this How are you fine? And magnitude is going in How will you consider this? While you analyze this What you will do? The current is moving like that This is the current Is length vector constant? No Every time length vector changes Here it is in this direction There it is in that direction Here it is in this direction So what you will do? You will take small, small lengths Like dL, dL lengths If you consider small length You will treat it as A uniform direction One direction thing So you have found out An expression for a straight wire For a curved wire You need to integrate Every dL you have to see Which direction the force is And accordingly you integrate Can you doubt on this? This wire On to which current is Magnetic field is inside This is basically a semicircular wire This distance is of course Two times the radius This is the center Magnetic field is given as B Find out The total force on this Curved wire Do this first You have Current like this The length is L only And current is I Magnetic field is B Fine From here to here A to B is L And B to C is also L This is 60 degree First do this then we will go there Not getting it? Can you see that Just combination of two Straight wires Find out force independently First on this and then on that Which direction the force will be Up or down? L cross B L is down And then you move Towards the B It is like this If you do like this L Then you have to go towards B L cross then B So it will be down L cross B This is length Keep it very simple L cross B L cross B So this is the force On A B Force on B C will be Like this So total force how will you find Will this force be Equal to this force in magnitude They are equal How much is the magnitude? I L into B Because current Length and magnitude They are perpendicular to each other And you will see that This component will get cancelled off From that component Vertical component get cancelled off But this component will get added up How much is this Angle 30 degrees Draw a line like this This will be 30 degrees This is also 30 degrees I L B Cos of 30 degrees Two times of that One from here Fine So this is the total force on the wire Getting it Any wire has mass M Then this force is equal to mass M acceleration Now try to do this Consider DLDL elements Here DLM You can come You can assume it to be straight This direction of force will be on this DL On just on this DL This is the DL vector This direction It will be inverse Right, directed towards the center So can you see that This vertical component get cancelled off From another similar element Over there Getting it Whose force is also like this This component will get cancelled off Right This component that is left is horizontal one Now let us zoom this This is the situation This is DL vector Fine And You have a force That is perpendicular to DL Like this You have to take its components Along horizontal direction Like this This will be equal to 90 meters theta Theta Again So this force value is how much Let us say this is df Sorry this will be df This will be df cos theta Right So only df cos theta We have to add What did you find So Because the vertical component df sin theta Will get cancelled off Fine So df cos theta Is the force Along x axis Fine And df cos theta is what I DL Into B Into cos theta Fine And now look at here Because I B into DL cos theta What is DL cos theta So DL cos theta becomes dy This is DL This length is DL cos theta Fine So now just imagine Here there is a DL You have to consider this length This length here Every time you are adding up the vertical lens So if you keep on adding vertical lens You will become 2R When you integrate Keep on adding vertical lens The total force will become I B Into total vertical lens Which is 2R Getting it In that case also In that case also How much is this length First tell me what is this length The half of the length This is 30 degree This is L So this is what L cos 30 I B into 12 cos 30 Vertical lens So you take any shape Of the wire You take this also If you know this distance Which is L The force, net force on this will be I B into L Now At times force The magnetic field will be given Like it will be given that the magnetic field B is 2 Tesla 1 Tesla and whichever direction it is But many a times Magnetic field will not be given directly Have you calculated magnetic field Due to various shape and size Straight wire, circle, solenoid Toroid, we found magnetic field So that magnetic field Which is coming I L cross B Or Q V into B May not be directly given And it need not be You may have to find out Using those formulae But that magnetic field Should not be Because of it's own current That magnetic field Should be external magnetic field Magnetic field of other Current Can create a force On the current Magnetic field due to the second wire Or second current can Create a force on the first current Like that But magnetic field due to the first current Can have a force on the first current itself It's like you applying force on yourself They will be equal in opposite force In the third law and get nullified Become zero So next topic is just that I mean just a small example is taken As in two Infinite wires are taken like this Draw these wires They are placed parallel to each other Distance Between The wires G The current over here is I1 And current over there is I2 You need to find The force On The L length of this wire L is the length Both are infinite though See the hint is You have to find magnetic field On this wire And then use I cross B How much is the magnetic field due to I1 On to I2 Due to an infinite wire what is the magnetic field You guys practice at home Like where you just throw your books away And then one week after you come here Class without looking at What is that Magnetic field is Mu naught I1 by 2 pi d What is the direction of this magnetic field On to I2 What is the direction of this magnetic field I am asking you something You have to speak up Tell me which direction is the magnetic field On I2 Obviously what I am asking you How good What do you think I what Why you are using this I have already told you Use that curve This thing Unnecessary you are confusing yourself I don't understand What is the point of teaching so much If you are still you are using What is confusing you And what is the point of you coming here How many times I told you Put your thumb along the wire And then curve your hand Which is going inside Magnetic field on to I2 Is inside Goes in And what is the direction of force on I2 Of this magnetic field Because of this magnetic field Direction of force What is the value of force How will you find the value of force Magnetic field is this The force is No I L cross B Cross B What is the direction of force On to I2 Because of this magnetic field Left or right Just check L is along the current L cross B So these two currents Are attracting each other I1 is Putting a force this way And I2 will be like Pulling it that way So there will be equivalent So The force will be what I2 L into B And we are perpendicular to each other L is like this B into the world So this is just multiplication of length And magnetic field This is the magnitude of force So magnitude of force is I1 I2 By 2 pi D Into L Now if you increase the length This length if you increase The force will increase I am saying this length is infinite The force will also grow infinite That has no meaning So we will just talk about force per unit length So F by L Is mu naught I1 I2 divided by 2 pi D Okay This is the force per unit length Newton per meter Newton magnetic type of moment Galonometer Till you guys do practice at home All of this is useless This is you just If you do not look at it After going on This will just evaporate You are coming here is useless If you do not do any problem practice I am just introducing you a concept Real learning happens When you sit alone in your home Practicing problems