Electric Charge & Coulomb's Law question from MHT CET 2026 (12 May, Shift 1)

Answer: (b)

1. $q$ at the centre is in equilibrium for any value. Each end charge $Q$ must also be in equilibrium.
2. Let separation be $2r$: $\dfrac{kQ^2}{(2r)^2} + \dfrac{kQq}{r^2} = 0$
3. $\dfrac{Q}{4} + q = 0 \Rightarrow q = -\dfrac{Q}{4}$
4. So the answer is (b) $-\dfrac{Q}{4}$.