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 460 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 190 N/C.

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


(b) What is charge Q?


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


(d) What is it on the outer surface?

Explanation / Answer

(a) The field at the surface is given by E = kq/r^2. putting E=460, k=9*10^9 and r=0.2 you get q=2.04*10^-9 C.

(b) Since field decreases Q must be negative. This time field is given by E=k(q-Q)/r^2. putting q=2*10^-9, r=0.2, k=9*10^9 you get q= -1.2*10^-9C.

(c) when the charge Q is inserted, -Q charge appears at the inner surface and +Q appears at the outer surface , hence the charge on the inner surface is +1.2*10^-9 C

(d) charge on the outer surface is 2.04*10^-9 - 1.2*10^-9 = 0.84*10^-9 C

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