A uniformly charged insulating spherical shell with total charge Q and radius R

Question

A uniformly charged insulating spherical shell with total charge Q and radius R is placed at the center of an irregular cavity within an electrically neutral chunk of metal. (See Fig. 3). (a) Determine the total charge on the inner and on the outer surface of the metal. (10 points) (b) Determine the electric field where possible based on the information provided. (Hint: No explicit integration needed here, just careful reasoning based on symmetry or the lack thereof) (10 points) (c) What if anything changes if the spherical shell is conducting and carries a total charge Q? (10 points) Figure 3

Explanation / Answer

(a)
Total charge on the inner surface, = - Q
Total charge on the outer surface, = + Q

(b)
Electric field inside insulating spherical shell = 0.
Electric field Outside = KQ/r^2

(c)
If the Spherical shell is conducting then,

Total charge on the inner surface, = - Q
Total charge on the outer surface, = + 2Q

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