A point charge inside a dielectric sphere

[eahaidar]

Hello again
I seen in this forum about this problem but not in the special case when the point charge is at the center of the sphere how do I solve the series legendre polynomials?

 

[mfb]

This is a simpler version of the general problem - you can apply the general solution, but you can just use the symmetry and the usual laws for electric fields (what exactly do you want to calculate?).

 

[eahaidar]

I need to solve the potential of a point charge in side a sphere of epsilon1 while outside with epsilon 2 if I use series solution I get r power over zero so I thought it's wrong any thoughts ??

 

[mfb]

Well r⁰ is just a constant.

You can simply use the symmetry and Gauß' law here.

 

[eahaidar]

But usually if they have same epsilon okay I can find the image charge and then find the potential but what happens with different epsilon ?

 

[mfb]

You try to make this way too complicated... there is no need for any image charge.