Question

A charge of magnitude q is divided into two parts such that force between resulting two charges is Maximum when separated through some distance r. The division of charges would be

Answer 1

Answer:

Let q is distributed as q

1

and (q−q

1

).

The force F=

r

2

K q

1

(q−q

1

)

=

r

2

K (q q

1

−q

1

2

)

Differentiating both sides w.r.to q

1

dq

1

dF

=

dq

1

d

r

2

K (q q

1

−q

1

2

)

=

r

2

K (q−2q

1

)

For maximum force

dq

1

dF

=0

⇒q−2q

1

=0

⇒q

1

=

2

q

and

(q−q

1

)=

2

q

So, charge will be

2

q

,

2

q

.