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 427 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 175 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

Here ,

a) let the charge is q

Using coloumb's law

E = k * q/r^2

427 = 9*10^9 * q/0.20^2

q = 1.898 *10^-9 C

the charge on the sphere is 1.898 *10^-9 C

b)

Now ,

for

174 = 9*10^9 * (1.898 *10^-9 + Q)/.20^2

solving for Q

Q = -1.124*10^-9 C

the charge Q is -1.124*10^-9 C

c)charge on inner surface = - Q

charge on inner surface = 1.124*10^-9 C

d)

charge on outer surface = q + Q

charge on outer surface = (1.898 - 1.124) nC

charge on outer surface = 7.74 *10^-10 C

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