Question

A point charge of +8 mu C sits at the center of a conducting shell of inner radius 12 cm and outer radius 15 cm, Which carries a net charge of -14 mu C. What is the charge on the inner strike of the shelf? What is the charge on the outer surface of the shell? What is the electric field at distance 20 cm from the center of the shell?

Answer 1

(a) Since the electric field in the bulk is zero.the charge in the middle and the charge on the inner surface must be zero. Therefore,the charge on the inner surface is –8 uC.

(b) We know the total charge on the metal sphere is -14uC , and this charge is divided between
the inner and outer surfaces. Therefore, the charge on the outer surface is -14 +8 = -6 uC

(c) Use Gauss’s Law.   $\int$^{E.dS = Q/$\epsilon$_o}

  E (4 pi r^2)= (-14+8)uC/$\epsilon$_o

E= (-6e-6 ) /[(8.85e-12)* 4 * 3.14 (0.2)^2 *]

E=-1349455 V/m