Originally Posted by

**Jason Bourne** I need help with this question,

A conducting sphere of radius **a** is surrounded by the electric potential

$\displaystyle F = \frac{Acos\theta}{r^2} + Crcos\theta$

where A and C are constants and $\displaystyle (r,\theta,\phi)$ spherical polar coordinates

1. confirm that F satisfies Laplace's equation. - i did this okay

2. If $\displaystyle \underline{E}=-\nabla F$ and $\displaystyle \underline{E} \rightarrow E_{0}\underline{e_{z}}$ as $\displaystyle r \rightarrow \infty $( $\displaystyle e_z$ being aligned with the line $\displaystyle \theta $= 0 ), determine the coefficient C

- here I got $\displaystyle C = -E_0$

3. If F=0 on the surface of the sphere, find A

- here I got $\displaystyle A = E_{0}a^2 $

4. **Calculate the electric field components **$\displaystyle E_r$** and **$\displaystyle E_{\theta}$** and evaluate them on the surface of the sphere. **- not sure how to do this I think I have to use Laplace's equation?

Thanks!