Method of images& half a sphere

AI Thread Summary
The discussion revolves around solving an electrostatics problem involving a half-sphere and the method of images. The initial approach involves placing a negative charge below the z=0 plane to cancel potential effects. The challenge arises in addressing the half-sphere, where a charge at the center was considered but complicated the z=0 plane. A breakthrough occurs when realizing that after placing the negative charge, the problem can be simplified by symmetrically placing additional charges to achieve zero potential on the sphere. The solution hinges on maintaining symmetry in the configuration of charges to satisfy the boundary conditions.
Ellyl
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Homework Statement


[PLAIN]http://img532.imageshack.us/img532/3751/39842434.png
Find the potential in all space for this configuration.

Homework Equations


..basic electrostatics stuff, I guess.


The Attempt at a Solution


I can easily cancel the whole z=0 plane by placing a charge of -q under it, of course, but I have no idea what I should do about the half-sphere. I naturally went for placing a charge in the center of the sphere to cancel the other two, and I attempted this by calculating the potential on the top of the sphere ([PLAIN]http://img15.imageshack.us/img15/6324/kqr.gif, if pythagoras was right) and negating that with another charge, but this naturally messes the z=0 plane. Is it some other configuration of charges that's symmetrical for the z=0 plane? I guess it has to be, but I have no idea what such configuration would also negate the potential of the sphere.
 
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..no, wait, I think I actually got this. Once I place the -q charge under the plane, the problem becomes equivalent to this:
[PLAIN]http://img189.imageshack.us/img189/6430/spherel.png
, and then I just need to place charges q' and -q' symmetrically to the z=0 plane so that the potential on the sphere equals zero. Right?
 
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