Question

A charge Q is divided into 2 parts such that they experience maximum electric repulsion where placed at a certain distance apart? Find the division?

Answer 1

Solution :

➡ Given:

↪ A charge Q is divided into two parts such that they experience maximum electric repulsion at a certain distance apart.

➡ To Find:

↪ Division of charge Q.

➡ Concept:

↪ For maximum repulsive force,

$\implies \sf \: \red{ \dfrac{dF}{dq} = 0}$

➡ Calculation:

• Let, charge q1 = q and charge q2 = Q - q

$\implies \sf \: F = \dfrac{kq(Q - q)}{ {r}^{2} } \\ \\ \implies \sf \: \dfrac{dF}{dq} = \dfrac{d}{dq} {\huge{(}}\dfrac{kq(Q - q)}{ {r}^{2} }{ \huge{ )}} = 0 \\ \\ \implies \sf \dfrac{d}{dq}{ \large{(}}q(Q - q){ \large{)}} = 0 \\ \\ \implies \sf \: \dfrac{d}{dq} (qQ - {q}^{2} ) = 0 \\ \\ \implies \sf \: Q - 2q = 0 \\ \\ \implies \sf \: Q = 2q \\ \\ \implies \: \underline{ \boxed{ \orange{\bold{ \sf{ \large{q_1 = q_2 = \frac{Q}{2}}}}}} } \: \bigstar$