A conducting spherical shell with inner radius a and outer radius b has a positi

Question

A conducting spherical shell with inner radius a and outer radius b has a positive charg Q located at its center. The total charge on shell is -3Q, and its isolated from its surroundings. (a) derive expressions for the electric field magnitude in terms of the distance r from the center for the regions r<a, a<r<b, and r>b (b) what is the surface charge density on the inner surface of the conducting shell? (c) what is the surface charge density on the outr surface of the conducting shell? (d) sketch the electric field lines and the loctaion of all the charges (e) graph the electric field magnitudes as a function of r

Explanation / Answer

a) r<a, qenc = Q so E = k Q/r^2

a<r<b, inside conductor so E = 0

r>b qenc = Q - 3Q = - 2Q

so E = 2k Q/r^2

b) since E = 0 inside

qenc = 0

so qinner = -Q

c) so total = - 3Q and -Q inside

so -2Q outside

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