Question

A charge Q is to be divided into two small parts. What should be the value of the charges on the parts so that the force between the points will be maximum ?​

Answer 1

Answer:

Let one part of the charge be q.

Thus other part of the charge is Q−q

Electrostatic force between them F=

r

2

kq(Q−q)

For maximum force,

dq

dF

=0

∴

dq

d

(

r

2

kq(Q−q)

)=0

Or

dq

d

(qQ−q

2

)=0

Or Q−2q=0 ⟹q=

2

Q

Hence force between them is maximum if the tqo parts have charge Q/2 each.