Question

A certain charge Q is to be divided into two parts (Q-q) and q.what is the relation of Q to q if the two parts,placed a given distance apartare to have maximium coulomb repulsion?

Answer 1

Two parts are   Q-q  and  q   placed at a given distance d (constant).
 K = 1/4πε

Coulomb's force of repulsion:  F =  K * q(Q-q)/d²
dF/dq = K/d² *  [Q - 2q]   = 0  for maximum force
          =>   q = Q/2

d²F/dq² = - 2 K/d²    < 0     Hence  Force is maximum for q = Q/2.

Answer 2

Answer:

Explanation:

F = 1/4πε × q (Q-q)/d²

For Electrostatic Force to be maximum, dF/dq = 0

=> d/dq {1/4πε × q (Q-q)/d²} = 0

=> Q × dq/dq - d/dq × 2q = 0

=> Q - 2q = 0

=> 2q = Q

=> q = Q/2