Torque on a Dipole. An electric dipole with dipole moment p is in a uniform external electric field E. (b) Which of the orientations in part (a) is stable, and which is unstable? (Hint: Consider a small rotation away from the equilibrium position and see what happens.)

Video transcript

Hey, everyone. Welcome back in this problem. We're told that alignments that offer zero torque. When a giant pool lies in an even external electric field are classified as stable and unstable, were asked to identify the stable and unstable alignments and were given the hint, what is the effect of a slight rotation for an equilibrium alignment? Alright. When we look at our answer choices, we see that the answer choices are relating the electric dipole moment P in the external electric field. E so let's think about those things. Recall that the torque the vector is given by the cross product of the electric dipole moment in the external electric field. E and if we want to write the magnitude of that torque, we can write this as P, the electric dipole moment times E, the magnitude of the electric field times sine of phi. So we're told in this problem that we have alignments with zero torque. So if our torque Tau is equal to zero, what does that mean? Well, P and E are non zero and so this sine of phi must be zero. Okay. First sign of fire to be zero, it must mean by is equal to 0° or five is equal to 180°. Okay. Now, if I think of the 0° then P and E are parallel. If I is equal to 180 degrees, then P and E are anti parallel. Okay, they lie the same plane pointing in opposite directions. So let's just write out those two options If Y is equal to zero P and E are parallel And if it's equal to 180°, the angle between the two, they are anti parallel. Alright, now we have to figure out which one is stable and unstable. Well, we know that if the electric dipole moment and the external electric field are parallel, then this is going to be stable. And what that means is that a small rotation of P, a small rotation of the electric dipole moment will cause a torque that's directed to bring P back into alignment with the okay. So we have a little change in P, we're gonna generate a torque and it's going to bring P back into alignment with the, in the other case, if we have finds 180 degrees P and E are anti parallel, this is unstable. Okay. Because if you have a small change in P, it's gonna generate a torque that is going to spin P to align it with E okay, that's unstable because it's going to be changing the direction of P okay. When there's a small change, it's gonna completely flip around into the other direction. Alright. So if we look at our answer choices, okay. A says that it is unstable when P and E are in the same direction and stable one, P and E are in opposite directions. That is not what we found, we found the opposite. And B it says that it is stable when P and E are in the same direction, stable when P and er in the opposite direction and unstable when P and er perpendicular. Okay. The first part of that is okay, but that second part is not what we found and see, we're told that it is stable when P and E are in the same direction. Okay when they're parallel, like we found an unstable when P and er in opposite directions when they're anti parallel, like we found. Okay. And so the answer here is going to be C We have stable one p and ear in the same direction or if they're parallel and unstable when they're in opposite directions or anti parallel. Thanks everyone for watching. I hope this video helped see you in the next one.