Question

A point charge 'Q' is placed at the centre of the line joining two equal charges '+q' and '+q'. The value of 'Q' when the system is in equilibrium is

• A. \(\frac{+q}{4}\)
• B. \(\frac{+q}{2}\)
• C. \(\frac{-q}{2}\)
• D. \(\frac{-q}{4}\)

Hint:

For a +q charge to be in equilibrium, the force from the middle charge must cancel the force from the other +q.

Answer 1

The Correct Option is D

Step 1: Forces on an end charge
Repulsion from the far +q is $kq^2/4a^2$, attraction toward Q is $k q|Q|/a^2$.

Step 2: Balance
$|Q| = q/4$, and it must be negative to attract.

Step 3: Answer
$Q = -q/4$, option (D).

Final Answer:
Option (D). \[ \boxed{-\frac{q}{4}} \]