Electric Field & Field Lines question from JEE Main 2022 (30 Jul, Shift 2)

Answer: (a)

1. Bent into a semicircle: $\pi R = L \Rightarrow R = \dfrac{L}{\pi}$, and $\lambda = \dfrac{q}{L}$.
2. Field at centre of semicircle: $E = \dfrac{2k\lambda}{R} = \dfrac{2}{4\pi\varepsilon_0}\cdot\dfrac{q}{L}\cdot\dfrac{\pi}{L}$
3. $E = \dfrac{q}{2\varepsilon_0 L^2}$
4. So the answer is (a) $\dfrac{q}{2\epsilon_0 L^2}$.