The electric field at point P just outside the outer surface of a hollow spheric

Question

The electric field at point P just outside the outer surface of a hollow spherical conductor of inner radius 10 cm and outer radius 20 cm has magnitude 425 N/C and is directed outward. When an unknown point charge Q is introduced into the center of the sphere, the electric field at P is still directed outward but is now 165 N/C.

(a) What is the net charge on and enclosed by the outer spherical surface before Q is introduced?
C

(b) What is charge Q?
C

(c) After Q is introduced, what is the charge on the inner surface of the conductor?
C

(d) What is it on the outer surface?
C

Explanation / Answer

a) qnet = Er^2/k = 425*0.04/9*10^9 = 1.89*10^-9 C = 1.89 nC

b) qtot = Er^2/k = 165*0.04/9*10^9 = 0.73*10^-9 C = 0.73 nC

Q = qtot - qnet = 0.73 - 1.89 = -1.16 nC

c) After Q is introduced, the charge on the inner surface of the conductor = -Q = +1.16 nC

d) charge on outer surface = -(1.16 - 0.73) = -0.43 nC

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