Two copper spheres A and B with radii of 20cm and 25cm respectively carry equal charge Q. Sphere A has a higher potential than sphere B due to its smaller size. When the spheres are connected by a copper wire, charge will flow from the higher potential sphere A to the lower potential sphere B until their potentials are equal. Therefore, the correct answer is that charge flows from sphere A to sphere B.

1. Physics Helpline
L K Satapathy
Electrostatics QA 3
Redistribution of Charge
Q Q
20cm 25cm
A B

2. Physics Helpline
L K Satapathy
Cells in Parallel
Electrostatics QA 3
Question : Two copper spheres A and B of radii 20cm and 25cm , separated
from each other , carry equal charge Q . When they are connected by a copper
wire , then
(a) Charge flows from A to B (b) Charge flows from A to B
(c) Charge flows from B to A (d) Charge flows from B to A
9
Q2
9
Q
9
Q2
9
Q
Concepts :
(i) Potential of a sphere of radius R
carrying charge Q , is given by
1
4 o
Q
V
R

(iii) When two charged spheres are connected , Charge flows from a body at
higher potential to a body at lower potential until their potentials are equal
(ii) When two spheres carry equal charges ,
the smaller sphere is at a higher potential
Q Q
20cm 25cm
A B

3. Physics Helpline
L K Satapathy
Cells in Parallel
Electrostatics QA 3
Answer :
Initial charge on each of A and B = Q
Let the final charge on A and B respectively are 1 2&q q
 Total charge of the system = 2Q
1 2 2 . . . (1)q q Q  
 Final potentials of the spheres are given by
1 2
1 2
1 1
&
4 4
A B
o o
q q
V V
r r 
  1 2[ 20 , 25 ]r cm r cm 
1 2
1 2
. . . (2)A B
q q
V V
r r
   
20cm 25cm
2q
1q
A B

4. Physics Helpline
L K Satapathy
Cells in Parallel
Electrostatics QA 3
Correct option = (b)
And Charge gained by sphere B 2
10
9 9
Q Q
q Q Q    
 Charge lost by sphere A 1
8
9 9
Q Q
Q q Q    
 Charge flows from A to B
9
Q
2
2
1 2
25 10
2 2
45 9
r Q
and q Q Q
r r
    

1
1
1 2
20 8
2 2
45 9
r Q
q Q Q
r r
     

1 2 1 2
1 2 1 2 1 2
2
(1)&(2)
q q q q Q
r r r r r r

   
 
1[ ]q Q
2[ ]q Q

5. Physics Helpline
L K Satapathy
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