Question : Two concentric conducting spheres are of radii r1 and r2. The outer sphere is given a charge q. The charge q' on the inner sphere will be (inner sphere is grounded) :
(1) q
(2) -q
(3) -q(r1/r2)
(4) Zero
Doubt by Nevaeh
Solution :
We know, whenever something is connected with the ground, its potential becomes equal to zero.
Potential on the surface of Inner sphere due to charge on its own surface
V1=kq'/r1
Potential on the surface of inner sphere due to the charge on the outer sphere
V2=kq/r2
Total potential on the surface of inner sphere will be zero so,
V1+V2=0
kq'/r1+kq/r2=0
kq'/r1=kq/r2
q'/r1=-q/r2
q'=-q(r1/r2)
Hence, the correct option is, (3) -q(r1/r2).
