Question

A solid conducting sphere of radius 2 cm has a charge of 8 μC. A conducting spherical shell of inner radius 4 cm and outer radius 5 cm is concentric with the solid sphere and has a charge of -4 μC Find:  

a) The electric field at r = 1 cm from the center of this charge configuration.  

b) The electric field at r = 3 cm from the center of this charge configuration  

c) The electric field at r = 4.5 cm from the center of this charge configuration.  

d) The charge in the inner and outer surface of the spherical shell.  

e) The electric field at r = 7 cm from the center of this charge configuration.  

Answer 1

a) E(4*pi*r^2) = q_enclosed/ $\epsilon _{o}$

Here

q_enclosed = 0

So

E = 0

b) Similarly

E = 9*10^9*8*10^-6/0.03^2 = 8*10^7 N/C

c) E = 9*10^9*8*10^-6/0.045^2 = 35.55*10^6 N/C

d) Inner shell = -q (induction) = -8uC

Outer Shell = q+Q = -4uC + 8uC = 4uC

e) E = 9*10^9*4*10^-6/0.07^2 = 7.347*10^6 N/C