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Question

A charge Q is divided into two parts of q and Qq. If the Coulomb repulsion between them when they are separated, is to be maximum, the ratio of Qq should be:
  1. 1/2
  2. 2
  3. 4
  4. 1/4

A
2
B
1/4
C
4
D
1/2
Solution
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Let parts are separated at a distance of 'd'
So repulsion force,
F=kq(Qq)d2
here, Q and d are constant so for maximum force differentiate the force w.r.t q,
dFdq=kd2(Q2q)
For maximum force, dFdq=0
kd2(Q2q)=0
Q2q=0
Qq=2

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