A charge divided into two parts "q" and "Q−q" and separated by a distance "R". The force of repulsion will be maximum when?
Answer: q = Q/2
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
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