Electromagnetism problem set 5 .pdf

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Problem set 5
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1. Consider a spherically symmetric charge distribution which has the radial dependence
 (r )  0e   r where alpha is a constant.
Find the potential and electric field using poisson’s equation. (Hint: total charge is Q)

2. A circular ring in xy plane carries a uniform line charge, find the first three terms

(n=0, 1, 2 for Legendre polynomials) in the multipole expansion for V.

3. Find the potential outside an infinitely long metal pipe, of radius R, placed at right angles to an
otherwise uniform electric field E0 , Find the surface charge induced on the pipe using V = 0 on
the yz plane, with E0 in the x direction.

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