There are two concentric metal shells of radii r 1 and r 2 (> r 1 ). If initially, the outer shell has a charge q and the inner shell is having zero charge and then inner shell is grounded. Find:
(i) Charge on the inner surface of outer shell.
(ii) Final charges on each sphere.
(iii) Charge flown through wire in the ground.
Text Solution
Verified by Experts(i) (r 1 ; (ii) Charge on inner shell; (iii) Charge flown in to the earth ; (i) potential of inner shell ; (ii) Final charges on spheres; (iii) initial charges on inner sphere
(i) (r 1 /r 2 )q
(ii) Charge on inner shell= –(r 1 /r 2 )q and charge on the outer shell = q
(iii) Charge flown in to the earth =(r 1 /r 2 )q
Sol.
Let charge q' appears on the inner shell after grounding
(i) potential of inner shell = 0 (grounded)
∴ 
– 
+ 
= 0
or 
= 
∴ q' = 
∴ charge on inner surface of outer shell ⇒ –q'
or ; k – q' = 
(ii) Final charges on spheres:
inner sphere → q' = 
outer sphere → q
(iii) initial charges on inner sphere = 0
final charges on inner sphere = q'
or charge flown from inner sphere to earth ⇒ – q' = 
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