A thin spherical shell with radius R 1 =3cm is concentric with a larger thin sph

Question

  A thin spherical shell with radius R1=3cm is concentric with a larger thin spherical shell with radius R2=5cm . Both shells are made of insulating material. The smaller shell has q1=+6nC charge distributed uniformly over its surface, and the larger shell has charge q2=-9nC distributed uniformly over its surface. Take the electric potential to be zero at an innite distance from both shells. (a) What is the electric potential due to the two shells at the following distance from their common center: (i) r=0 ; (ii) r=4cm ; (iii) r=6cm ? (b) What is the magnitude of the potential difference between the surfaces of the two shells? Which shell is at higher potential: the inner shell or the outer shell?

Explanation / Answer

potential of outer shell

But, charge distribution outside a shell is equivalent to point charge at the center of the shell

net chage of the 2 shells= q1+q2=-3 nC

So, Vo = k*(-3) /R1= -540 V

potential between 2 points= k*q*(1/r1 - 1/r2) for r1<r2

potentai of inner shell= potentail of outer shell +k*q1*(1/R1 - 1/R2 ) = -540+720= 180 V

(i) r=0 cm is inside the inner shell. As before

potential at (r=0)= potential of the inner shell {since there is no charge inside the inner shell)

potentail= 180V

ii)r=4 is between the inner and outer shell

potentail= potentail of outer shell + k*q1*(1/R -1/R2) =270-540 =-270 V

iii) r=6 is beyond the outer shell

potential= k*q/r ; q-net charg-3 nC

            = -450 V

b) potentail difference between 2 shells= 720 V

Inner shell is at higher potential

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