Electrodynamics/Tutorials/3/4/4

Video Intro

Hi, this is Jonathan Gardner.

We're covering [section reference] of Griffiths Introduction to Electrodynamics.

I'm going to move fast, but you can always rewind.

Thumbs up and share if you appreciate my effort.

As always, questions in a video response or comments.

Let's get started.

Electric Field of a Dipole

Let's start with a charge geometry with dipole moment p.

THe potential is r hat dot p, which is simply p cos theta, the angle between p and r that goes to the point P we are interested in.

(formula)

The field is the negative of the gradient of the potential:

(formulas for Er, Etheta, Ephi)

Thus, E is:

(full formula of E)

Note that the field falls off at 1/r^3, compared to 1/r^2 for a point charge.

You might expect, and you'd be correct, that quadrupoles fall off at 1/r^4, octopoles, 1/r^5, etc...

This isn't surprising: the electric field is always 1/rth the potential -- the gradient's d/dr adds in another 1/r.

When theta is 0 or pi, then the electric field points in the same direction as r. When theta is pi/2, then the field points in the theta direction -- downwards.

It looks something like this.

(Draw)

For comparison, here's the field of a "physical" dipole:

(draw)

The difference is rather obvious: the bit near the point charges simply compress and disappear in a "pure" dipole.

Conclusion of Chapter 3

That's it for Chapter 3. In Chapter 4 we're going to see how insulators, also known as dielectrics, behave in electric fields. Hint: They're tiny dipoles!

Thanks for your time.

Next

Previous