A source consists of a point charge 30 nC at the center of a

A source consists of a point charge 30 nC at the center of a spherical CONDUCTING shell of inner radius a - 0.02 m and outer radius b - 0.03 m which has a charge >10 nC, as shown in the figure. Assume that if the shell is a conducting medium in electrostatic equilibrium, then E_r = 0 for a

Solution

a)Take the inner surface and apply Gauss law on it

so 30nC+charge on inner surface = 0 (since electric field is zero inside conductor)

so charge on inner surface = -30nC

Now since charge remains conserved so

-30nC + charge on outer surface = -10nC

so charge on outer surface = -10+30=20nC

b) for r<a

using gauss law for r<a electric field = Qinside/(e0*4*pi*r^2)=9*10^9*30*10^-9/r^2=270/r^2

for r>b

electric field = Qinside/(e0*4*pi*r^2) = 9*10^9*(30-30+20)*10^-9/r^2=180/r^2