Question

The potential at the surface of a sphere (radius R) is given by Vo=Kcos3D, Where D...

The potential at the surface of a sphere (radius R) is given by Vo=Kcos3D, Where D is theta,K is a constant. Find the potential inside and outside the sphere, as well as the surface charge density s(D) on the sphere.(Assume there is no charge inside or outside the sphere).

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Answer #1

The potential inside and outside must have a form

(1)

By continuity of the potential,

The normal component of the electric field is discontinuous by / ,   

Thus,

We can find Al ,

Since is constant, A0 = R/0 and is 0 for all other . Then the potential is given by

  

(2)

The potential at the surface of a sphere (radiusR ) is given by

  

   (3)

First, notice that . Potential is given by Eq. 1. One can find Al by comparing with .

  

The charge density

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