Question

Two spherical conductors B and C having equal radii and carrying equal charges in them repel each other with a force , when kept apart at some distance. A third spherical conductor having same radius as that of B but uncharged, is brought in contact with B, then brought in contact with C and finally removed away from both. The new force of repulsion between B and C is:

A

B

C

D

Hard
Solution
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Correct option is D)

 
Let and have charge   each initially and are seperated by distance.
From Coulomb's law, force between them            


When an identical uncharged spherical conductor  is brought in contact with charged sphere .
By symmetry, the total charge will be shared equally among them, as both have equal radii.
  Charge on and             

Now, when the conductor is brought in contact with
They will also share equal charge among themselves, as both have equal radii.
 Charge on   and  

 
New coulomb force between   and :

From equation , we get:

Hence, Option D is correct

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