Griffiths Example 3.8

1. Feb 17, 2008

ehrenfest

[SOLVED] Griffiths Example 3.8

1. The problem statement, all variables and given/known data

In Example 3.8, Griffiths makes two claims without justification that I want justification for. First, he says that V=0 in the equatorial plane (I assume this means that x-y plane). Second, he says that $$V \to -E_0 r \cos{\theta}$$ for $$r >>R$$. Where does the cosine come from?

2. Relevant equations

3. The attempt at a solution

2. Feb 17, 2008

Biest

The problem is originally defined in cartesian coordinates. Now that we are using the Legendre Polynomials it has to be in spherical coordinates.

Orginally:
$$V \to -E_0 z$$
goes to
$$V \to -E_0 r \cos{\theta}$$
since
$$z = r \cos{\theta}$$

3. Feb 17, 2008

ehrenfest

And how do you know V=0 all over th equatorial plane?

4. Feb 17, 2008

Biest

It is an uncharged metal sphere, so we basically assume it was grounded beforehand

5. Feb 17, 2008

ehrenfest

I see. Thanks.