Question

A given charge \( Q \) is divided into two parts which are then kept at a distance \( d \) apart. The electrostatic force between them will be maximum if the two parts are

• A. \( \frac{Q}{4} \) and \( \frac{3Q}{4} \)
• B. \( \frac{7Q}{8} \) and \( \frac{Q}{8} \)
• C. \( \frac{Q}{3} \) and \( \frac{2Q}{3} \)
• D. \( \frac{5Q}{6} \) and \( \frac{Q}{6} \)
• E. \( \frac{Q}{2} \) each

Hint:

Product \( x(Q-x) \) is maximum when both are equal.

Answer 1

Answer: (E)

Concept: \[ F \propto q_1 q_2 \]

Step 1: Let charges be \( x \) and \( Q-x \).
\[ F \propto x(Q-x) \]

Step 2: Maximize.
Maximum when: \[ x = \frac{Q}{2} \]