Question

Two spherical shells have a common center. A -2.5  10^-6 C charge is spread uniformly over the inner shell, which has a radius of 0.050 m. A +5.7  10^-6 C charge is spread uniformly over the outer shell, which has a radius of 0.15 m. Find the magnitude and direction of the electric field at the following distances (measured from the common center).

(a) 0.20 m

magnitude	---Select--- N/C C/N N C
direction	---Select--- radially inward no direction radially outward

(b) 0.10 m

magnitude	---Select--- C/N C N/C N
direction	---Select--- radially outward no direction radially inward

(c) 0.025 m

magnitude	---Select--- N C/N C N/C
direction	---Select--- radially outward no direction radially inward

Answer 1

The problem can be solved using the Gauss theorem in electrostatics.

Given,

With the charges distributed about the spherical surfaces, the Gaussian surface will also be spherical in nature. Therefore Gauss law is given by,

where

E is the electric field (N/C)

a) Given, r = 0.20m - corresponds to a point outside the outer shell

Since the total charge enclosed is positive, the direction of electric field will be radially outwards the outer shell

radially outwards (Ans.)

b) Given, r = 0.10m - corresponds to a point in between the inner shell and outer shell

Since the total charge enclosed is negative, the direction of the electric field will be radially inwards

radially inwards (Ans.)

c) Given, r = 0.025m - corresponds to a point inside the inner shell

Since the total charge enclosed is zero, there will be no electric field inside the inner shell

no direction   (Ans.)