Torque on a Dipole. An electric dipole with dipole moment p is in...

Question

Torque on a Dipole. An electric dipole with dipole moment p is in a uniform external electric field E. (a) Find the orientations of the dipole for which the torque on the dipole is zero.

Accepted Answer

welcome back everybody. We have a group of students that is setting up a di pole inside of an electric field and they are going to do that by taking a die pool like this with two charged spheres and then inserting it into this electric field which I have drawn here Now we are tasked with finding what alignments of the di pole in comparison to the electric field lines. Give us a torque of zero. What alignments here. So what do they mean by alignments? What they really mean is how, not necessarily the positions because the field is uniform, but really the angle, What is the angle that we're looking for between? Say we have our di pole right here. What is this angle going to be between the di pole and the electric field lines? Well, the formula for torque as a vector is equal to the cross product of the di pole vector crossed with the magnetic field line vectors. This is equal to P. E. Times the sine of theta. And we need to see when this is equal to zero. E. And E are just going to be numeric values. So those are just gonna disappear. And then you take the arc sine of both sides and you get something like this. That data is equal to the arc sine of zero. Which if you have your calculator set two degrees, make sure you do. You will get that. This is zero degrees and 180 degrees. So what does this mean? Right. Well, I'm gonna redraw our electric field lines, right? It's going to look something like this. And in order for us to have zero degrees or 180 degrees, we're either going to have this meaning that the lines are parallel and they're zero degrees or they are anti parallel as in they are parallel but they are going in different directions. Let me label those just so that we are clear that either having a parallel setup or an anti parallel setup will lead us to having a torque of zero, which corresponds to our answer choice of E. Thank you all so much for watching. Hope this video helped. We will see you all in the next one.

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