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 Experts(i) on inner shell ; (ii) Heat produced during the process
(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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