Electric Field & Field Lines question from MHT CET 2024 (11 May, Shift 2)

Answer: (a)

1. Opposite pairs $A, D$ ($+q, +q$) and $C, F$ ($-q, -q$) cancel at $O$.
2. Field of the five charges = field of $-q$ at $B$: $\dfrac{kq}{r^2}$ towards $B$.
3. Field of $+Q$ at $E$: $\dfrac{kQ}{r^2}$, also towards $B$.
4. $\dfrac{kq}{r^2} = 3\dfrac{kQ}{r^2} \Rightarrow Q = \dfrac{q}{3}$
5. So the answer is (a) $\dfrac{+q}{3}$.