Question

A solid insulating sphere of radius 5.00 cm is centered at the origin. It carries a total charge of 2.00 C uniformly distributed through its volume. Concentric with this sphere is an uncharged conducting shell whose inner and outer radii are 8.00 cm and 10.0 cm respectively.  

a What is the electric field (magnitude and direction) 1.00 cm from the origin  

b How much charge resides on the inner surface of the conductor 

c What is the electric field (magnitude and direction) 9.00 cm from the origin 

d What is the potential (with respect to infinity) at the inner surface of the conducting sphere

Answer 1

We use spherical gaussian symmetry to find the electric field that is

a) at r = 1cm

EA = Q/_o

here A = 4 * 3.14 * (0.01)² = 1.25E-3m²

The charge contained is the charge of the insulating sphere; Q = V

= {2/ [(4/3) * 3.14 * (0.05)³] } * [(4/3) * 3.14 * (0.01)³] =1.6*10^-2C

so, E = (1.6*10^-2 )/ (1.25*10^-3 *8.85*10^-12) = 1.44E12 N/C

b) charge on the inner surface of the conductor = -1.6*10^-2C

c) E = 0

d) V =             = k Q/0.01 = (9*10⁹ * 1.6*10^-2)/0.01 =1.44*10¹⁰ V