A solid, insulating sphere of radius R1=5cm carries a charge density =16nC/cm3 a

Question

A solid, insulating sphere of radius R1=5cm carries a charge density =16nC/cm3 and is surrounded by a thin conducting spherical shell of outer radius R2=12cm. The conducting shell carries a total charge Q=1.2C.

(a) Calculate the intensity of the electric field at a distance r=4cm from the center of the insulating sphere.

(b) Calculate the total electric potential at the surface of the insulating sphere.

(c) Calculate the charges on the inner and outer surfaces of the conducting shell.

(d) Calculate the intensity of the electric field at the outer surface of the conducting shell.

Explanation / Answer

(a) Electric field = kq/r2
q = 16*43/53 = 8.192 nC
E = 9*109*8.192*10-9 / (4*10-2)2 = 46080 N/C
(b) Potential = Kq/r = 9*109*(8.192*10-9) / (4*10-2) = 18.432*102 V
(c) on inner surface charge = 16*(4/3)*Pi*53  = -8.378 uC
On outer surface = 8.378 + 1.2 = 9.578 uC
(d) E = kq /r2 = 9*109*(9.578*10-6) /(12*10-2)2 = 5.986*106 N/C

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