A solid insulating sphere of radius a = 5.3 cm is fixed at the origin of a co-or

Question

A solid insulating sphere of radius a = 5.3 cm is fixed at the origin of a co-ordinate system as shown. The sphere is uniformly charged with a charge density ? = -159 ?C/m3. Concentric with the sphere is an uncharged spherical conducting shell of inner radius b = 14.5 cm, and outer radius c = 16.5 cm.

What is V(b), the electric potential at the inner surface of the conducting shell? Define the potential to be zero at infinity.

I have found that the answer must include the conducting sphere (r = c, rather than b) but I haven't been able to figure out why that is?

Explanation / Answer

Vb = Vb-Vinfinity =    - integral from infinity to b of E.dl

to calculate Vb we need to know the electric field outside the shell

so , it will be KQ/r2

inside the shell E=0

so, Va = - - integral from infinity to c of E.dl- - integral from infinity to b of E.dl

so, Va = KQ/c

where K =9x109 ,Q=(4/3) * pi * 0.0533 *-159 C=9.91x10-11C

C=0.165m

hence,Va = KQ/c =5.405 V

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