00:01
We're going to be looking at the potential of a dipole.
00:04
And a reminder of what a dipole is, is it is two equal and opposite charges.
00:11
For the sake of argument, i'll line them up on the x -axis, and put a positive cue on one side and a negative cue on the other.
00:22
The dipole moment, for historical reasons, points from the negative to the positive charge.
00:30
And that's really to kind of make the electric field look a little bit continuous.
00:40
So if we draw the electric field, it is going to point out of the positive charge and into the negative charge.
00:50
And i'll just show it on the axis, because what we're really most interested in is the potential.
00:57
And what the equal potentials look like is essentially they look kind of like, like distorted point charge potentials.
01:12
They aren't perfect circles.
01:14
They're kind of distorted a little bit because of the fact that the two charges.
01:20
And then they start to flatten out in the middle.
01:25
And what we know is that if you are closer to the positive charge, you have a high potential, which is usually positive relative to the zero that you expect at infinity.
01:38
And it is going to be negative near the negative charge.
01:44
Now, all this is well and good.
01:47
What we're going to be doing is collapsing the positive and negative into something called a point dipole, which is an approximation.
01:59
So you're going to shrink it down so you can't see the distance between the two.
02:05
By the way, that magnetic, not magnetic, electric dipole moment is a product of the charge on any single one of the charges, just put the positive one in there, times the d vector joining the negative to the positive.
02:24
So that's called the dipole moment.
02:29
And why that is useful is you can ignore the fact that there's a physical separation between the two points and collapse it to a single point so that you don't really care about that distance anymore, but you do care which way that dipole moment is pointing.
02:53
And it turns out that if you start with the potential total as the sum of the two potentials in the system above.
03:07
So you're adding the v plus to the v minus.
03:11
And you make an approximation at very large distances, r being much, much greater than the separation between the two points that are in the 24 point dipole.
03:27
Then you get an approximation for the, the dipole potential that's fairly easy to work with.
03:35
It varies as 1 over 4 pi epsilon knot.
03:38
No surprise there.
03:40
The point charges have that in there.
03:43
The dipole moment shows up in the numerator and the denominator shows up as a r squared.
03:55
And then there is an angular dependence that takes care of the fact that the equipotentials really do matter concerning where you are in terms of the axis of the dipole, the way it's lined up.
04:13
And that dependence goes as cosine theta, where theta, the way i've drawn it, fortunately, puts theta the angle with the positive x axis.
04:27
But your dipole could be oriented any possible which way.
04:31
So it's important to note that theta is the angle between the axis, the positive side of the dipole, and the point of observation.
04:50
Okay.
04:51
So it will be clear that you have a negative potential when you're over on one half of the dipole...