Question

A charge \( Q \) is to be divided between two objects. The values of the charges on the objects so that the electrostatic force between them will be maximum is:

• A. \( \frac{Q}{2}, \frac{Q}{2} \)
• B. \( \frac{Q}{3}, \frac{2Q}{3} \)
• C. \( \frac{Q}{4}, \frac{3Q}{4} \)
• D. \( \frac{Q}{5}, \frac{4Q}{5} \)

Hint:

To maximize product \( q(Q - q) \), set \( q = \frac{Q}{2} \) — this makes both charges equal.

Answer 1

The Correct Option is A

Let charges on the two objects be \( q \) and \( Q - q \). Electrostatic force: \[ F = k \frac{q(Q - q)}{r^2} \] To maximize force, differentiate: \[ \frac{dF}{dq} = k \frac{(Q - 2q)}{r^2} = 0 \Rightarrow Q - 2q = 0 \Rightarrow q = \frac{Q}{2} \] So, charges are \( \frac{Q}{2} \) and \( \frac{Q}{2} \)