Two concentric hollow conducting spheres of radius a and b (b>a) contains charges Q a and Q b respectively. If they are connected by a conducting wire then find out following
(i) Final charges on inner and outer spheres.
(ii) Heat produced during the process.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(i) on inner shell = 0, on outer shell = Q a + Q b
(ii ) 
Sol.
Before connecting spheres charges are Q a & Q b on inner & outer sphere
After closing switch S:
Potentials of both becomes equal
Let charges on two spheres after connection are Qa' & Q b ' as shown
∴ Q a ' + Q b ' = Q a + Q b ...........(1)
V I = V II
∴ 
+ 
= 
+ 
∴ Q a ' = 0 ...........(2)
Putting (2) in (1)
0 + Q b '= Q a + Q b
∴ Q a '= Q a + Q b Ans.
i.e total charge is transferred to outer shell
(ii) Heat produced during the process ⇒ Initial energy of system – final energy of system
⇒ Heat = Vi – Vf
= 
– 
= 
+ 
+ 
– 
(Q a + Q b ) 2 n
= 
+ 
+ 
– 
– 
– 
= 
. 
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