# Method of image charges

1. Feb 17, 2009

### the_viewer

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

We have a conducting and grounded wall for $$z<0$$, so $$\Phi=0$$ for $$z<0$$. In front of this wall, we place a homogeneous charged sphere with radius $$R$$ and total charge $$Q$$. The center of the sphere has a distance of $$a$$ to the front of the wall.

I need to find the electrostatic potential $$\Phi(\vec{x})$$ for $$z>0$$ with the method of image charges.
I just need the potential outside the sphere. I do not need to determine the potential inside the sphere.

So... Where do I place the image charges?

2. Relevant equations

All electrostatic equations.

3. The attempt at a solution

I placed a first image charge in the center of the sphere, because a charged sphere acts like a point-charge in it's center. So I can replace the sphere with a single point-charge.
Then I added a second image charge inside the wall with opposite charge $$-Q$$. This second charged is placed exactly symmetrical to the first image charge.
So... if the first charge is placed by $$z=a$$, I have placed the second at $$z=-a$$.

Is this a correct/possible solution for this problem? Or do I need some different approaches here, because the wall has an effect on the charge on the sphere?

Last edited by a moderator: May 4, 2017
2. Feb 17, 2009