Question

Suppose you have three identical metal spheres, A, B, and C Initially sphere A carries a charge q and the others are uncharged. Sphere A is brou contact and separated. Finally spheres A and C are brought in contact and then separated.

Answer 1

The charge on sphere A and C is
`(3q)/(8) C`

Solution:

As per the question:

Charge on sphere A = q C

Now,

When sphere A with 'q' charge is brought in contact with B then conduction takes place and equal charges are distributed on both the spheres as:

`(q + q)/(2) = (q)/(2)`

Charge on each A and B is
`(q)/(2)`

Now, after separating both the spheres, when sphere B with charge
`(q)/(2)` touches uncharged sphere C, again conduction occurs and the charge is distributed as:

`((q)/(4) + (q)/(4))/(2) = (q)/(4)`

Now, after the charges are separated with charge
`(q)/(4)` on each sphere B and C

Now,

When sphere A and Sphere C with charge
`(q)/(2)` and
`(q)/(4)` comes in contact with each other, conduction takes place and charge distribution is given as:

`((q)/(2) + (q)/(4))/(2) = (3q)/(8)`