Moving Charge in a Magnetic Field question from JEE Main 2025 (22 Jan, Shift 2)

Answer: (a)

1. Circular orbit: $r = \dfrac{mv}{eB} \Rightarrow mv = eBr$.
2. Bohr condition: $mvr = \dfrac{nh}{2\pi} \Rightarrow eBr^2 = \dfrac{nh}{2\pi} \Rightarrow r = \sqrt{\dfrac{nh}{2\pi eB}}$.
3. First excited state: $n = 2$, so $r = \sqrt{\dfrac{h}{\pi eB}}$.
4. So the answer is (a).