Energy Stored & Force between Plates question from MHT CET 2023 (10 May, Shift 1)

Answer: (a)

1. Field between plates: $E = \frac{\sigma}{\varepsilon_0} = \frac{q}{\varepsilon_0 A}$.
2. Energy density $u = \frac{1}{2}\varepsilon_0 E^2 = \frac{1}{2}\varepsilon_0 \cdot \frac{q^2}{\varepsilon_0^2 A^2}$
3. $u = \frac{q^2}{2\varepsilon_0 A^2}$
4. So the answer is (a) $\frac{q^2}{2\varepsilon_0 A^2}$.