# Math Help - calculate electric field components, simple

1. ## calculate electric field components, simple

I need help with this question,

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

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

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

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

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

- here I got $C = -E_0$

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

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

4. Calculate the electric field components $E_r$ and $E_{\theta}$ 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!

2. Originally Posted by Jason Bourne
I need help with this question,

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

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

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

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

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

- here I got $C = -E_0$

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

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

4. Calculate the electric field components $E_r$ and $E_{\theta}$ 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!
Presumably, if you have already done (2), then you have already solved for $E(r,\theta)$. Evaluate that for r= a and separate into r and $\theta$ components.

3. Originally Posted by HallsofIvy
Presumably, if you have already done (2), then you have already solved for $E(r,\theta)$. Evaluate that for r= a and separate into r and $\theta$ components.
Yeah, that's what I thought originally, I got

$\underline{E} = (\frac{2Acos\theta}{r^3} -Ccos\theta)\underline{e_r} + (\frac{Asin\theta}{r^3} +Csin\theta)\underline{e_{\theta}}$

then evaluate at r=a and seperate into the right components as you say but this part of the question seems to be worth more (its from a past exam paper) than the other parts so I figured that would be far too easy!

But I'm not sure what else to do so wondered if anyone knew what else I could do for this?