 Let's work out some numericals on electric potential due to dipoles. So here's the first one We are given a dipole. There's a point dipole, tiny dipole, whose moment is given to be 3 times 10 to the minus 8 coulomb meter This is not centimeter. This is coulomb meter, and we are asked to calculate what the potential is going to be at Distance of 2 meters from that dipole along the axis So how do we do this? Well in a previous video, we already derived what the expression for the potential due to a dipole Anywhere is. So let me quickly show you that. We saw that if you have a dipole, let's say there's a negative charge There's a positive charge Separated by some distance we used to call 2a and if you want to know what their potential at some point p At a distance r from the center center of the dipole This then we saw that that expression is going to be K q into 2a 2a cos theta where theta is this angle theta divided by divided by r squared And how did we derive that? Well, we calculate what the potential there here is going to be due to this charge Potential here is going to be due to this charge We added them and then we we did some mathematics where we said, okay Let's assume that p is to be very very far away and if you need some clarity or you need a refresher on where? How did we derive that? Where does it all come from? The great idea to positive studio go? It'll be a great idea to go back and watch our video on the derivation of electric potential due to dipoles But anyways, let's continue What's given to us is we don't we're not given Q we're not given the distance we're given the dipole moment and we've given some vector. What is that? We'll remember that this product itself is what we call This product product of charge and the distance that itself is what we call the dipole moment, which we represent as p and What is that direction say direct? The dipole moment is taken to be a vector and its direction is always from the negative charge to the positive charge So this this is your negative charge. This has got to be your positive charge. So in here dipole moment is this way Okay, and so you know To think about that angle the theta is the angle between the dipole moment vector and the vector That points towards p the r vector and the dipole moment vector. That's our angle All right So why don't you pause the video and see with this now? Can you go ahead and solve this particular problem? All right So let's do this So what is K? K is that familiar 1 over 4 pi epsilon not whose value is 9 times 10 to the power 9 and I don't know the charge or 2a, but I know the total product. That's dipole moment That's given to me as 3 times 10 to the power minus 8 and What is cos theta over here? What is theta? Well theta is this angle in our case notice if I were to draw that vector from here to here That angle is 0 the two are aligned. So cos 0 write that cos 0 divided by r square r is this distance 2 meters. So 2 square is 4 It's in meters. So I don't have to do any conversion and There therefore I all I have to do now is solve this. So I get cos 0 is 1 So this will be 27 This will be 10 Divide by 4 so that's 270 by 4 That gives me 4 6 are 24 3 carries 30 47 are 28 2.5 and There you have it 67.5 volt. That's the potential here. We're getting a positive sign. Does that make sense? It's positive Yeah, because the point is closer to the positive charge and a little farther away from the negative charge So it makes sense that we're getting a positive voltage Let's try a second one again We're given a dipole this time we have charges given the distance between the dipole is given We have to find the potential at point P at a distance 10 meters from the dipole and again notice that this is a point Dipole this distance is much smaller compared to this so we can use the far away approximation the same Thing that we did here So again, can you pause the video and try solving this one on your own? All right, let's do this. So we'll just substitute this value So you get VP is equal to K is 1 by 4 pi epsilon naught. That's 9 times 10 to the power 9 Q is the charge that's given and remember we just have to calculate Put in the magnitude of the charge the sign is already baked in when we derived the formula So just the magnitude so 3 times 10 to the power minus 6 minus 6 because it's a micro micro is 10 to the minus 6 and Times 2a now one of the mistakes I used to make while substituting over here is to a I used to put two times say one 1 millimeter, but it's not this itself is to a remember to a is a distance between the two charges Okay, so 1 millimeter itself is my 2a So it's one and a milli milli is 10 to the minus 3. So let's take care of ours Let's take care of our 10 powers times cos theta. Hmm What is cos theta? Well, there's a 60 So we might write cos 60 That's wrong. It's not cos 60. Can you pause and think a little bit about why it's not cos 60? Alright, let's see. What is theta again? Remember theta is the angle between the dipole moment vector which starts from negative charge to the positive charge and The R vector. So over here. What is our dipole moment vector? So dipole moment vector is from negative charge to the positive charge. It's downwards this way This is our dipole moment vector and our R vector is this way towards P And so notice the angle is the angle theta is this angle And that's not 60. The whole angle is 180. So this is 180 minus 60. So that's our theta 180 Minus 60. So let's correct that So that gives us 180 I mean, I can just write 120, but I like to do I like to calculate this way using our What do you call that? Alar angles? Yeah. Alar angles. I think that's the term. But anyways, so divided by R square. What is R? R is 10 meters. So it's going to be It's going to be 10 square. That's 100 So let's see. We just now have to plug in. So nine times three is 27 times This this and this cancels out see 10 to the power nine minus six minus three minus nine that nicely cancels out What is cost of 180 minus 60? Hmm. Well, I remember the Alar angles thing if cost of 180 minus theta is Since this is in the second quadrant. I write A S T C So in second quadrant cost is negative. So it's going to be minus cost 60. So this is going to be minus cost 60 And cost 60 is half. So I'll get minus half over here divided by 100 And that's going to be 27 by two, which is what is that? 17 18.6 no 13.5 So it's negative 13.5 divided by 100 So that's minus point 135 volt And so let's think about does it make sense that we're getting a negative sign over here? Yeah, because this time notice that point P is a little closer to the negative charge Compared to the positive charge. So even if we had wrongly substituted at this as cost 60 and gotten a positive value We could just look over here and say hey, that's supposed to be negative And then I could have like realized why am I getting a positive value and I could have gone back and corrected myself