A charge divided into two parts "q" and "Q−q" and separated by a distance "R". The force of repulsion will be maximum when?

A charge divided into two parts "q" and "Q−q" and separated by a distance "R". The force of repulsion will be maximum when?

Explanation

The electrostatic force between two charges is given by Coulomb’s Law:

F = k * q₁ * q₂ / R²

If a total charge Q is divided into two parts: q and Q−q, the force becomes:

F = k * q * (Q − q) / R²

To maximize F, differentiate F with respect to q and set dF/dq = 0:

dF/dq = k/R² * [Q − 2q] = 0  

⇒ Q − 2q = 0  

⇒ q = Q/2