Moving Charge in a Magnetic Field question from MHT CET 2025 (19 Apr, Shift 2)

Answer: (c)

1. Magnetic force gives circular motion: $r = \dfrac{mv}{qB}$.
2. Bohr condition: $mvr = \dfrac{nh}{2\pi} \Rightarrow \dfrac{(mv)^2}{qB} = \dfrac{nh}{2\pi} \Rightarrow (mv)^2 = \dfrac{nhqB}{2\pi}$.
3. $E = \dfrac{(mv)^2}{2m} = \dfrac{nqBh}{4\pi m}$
4. For $n = 2$: $E = \dfrac{qBh}{2\pi m}$. So the answer is (c).