Question

A conducting spherical shell with inner radius a and outer radius b has a positive point charge Q located at its center. The total charge on the shell is -3Q, and it is insulated from its surroundings (Fig. P22.44) (a) Derive expressions for the electric-field magnitude E in terms of the distance from the center for the regions r < a, a < r < b, and r > b. What is the surface charge density (b) on the inner surface of the conducting shell: (c) on the outer surface of the conducting shell? (d) Sketch the electric field lines and the location of all charges. (e) Graph E as a function of r.

Answer 1

Since the charge inside the shell is Q, the inner surface with radius 'a' will have -Q charge evenly distributed on it.

Also it is given that the net charge on the shell is -3Q, so the charge on outer surface has to be -2Q.

Since net charge for r < b is zero, hence the electric field will be zero for r < b.

For r>b, the net electric field is -3Q, so the electric field will be given by formula E = (-3Q)/(4*pi*e*r^2)