A solid, insulating sphere of radius a has a uniform charge density throughout i

Question

A solid, insulating sphere of radius a has a uniform charge density throughout its volume and a total charge of Q. Concentric with this sphere is an uncharged, conducting hollow sphere whose inner and outer radii are b and c as shown in the figure below. We wish to understand completely the charges and electric fields at all locations. (Assume Q is positive. Use the following as necessary: Q, o, a, b, c and r. Do not substitute numerical values; use variables only.) Conductor (a) Find the charge contained within a sphere of radius- (b) From this value, find the magnitude of the electric field for , (c) what charge is contained within a sphere of radius r when , (d) From this value, find the magnitude of the electric field forwhen (e) Now consider r when b

Explanation / Answer

a) Qin = 2Q/4pia^3 * 4/3pir^2
= 2Qr^3/a^3

b) E = Qin / A*E0

= (2Qr^3/a^3) / (4pir^2E0)

= Qr/2piE0a^3

= 2KQr/a^3

c) a<r<b
Qin = 2KQ

d)
E = 2KQ/r^2

e)
b<r<c
E = 0

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