JEE Main · 2026 · 02 Apr 2026 · Shift 2 · Modern Physics

Using Bohr's model, calculate the ratio of the magnetic fields generated due to the motion of the electrons in the

2^{nd}

and

4^{th}

orbits of hydrogen atom.

Answer: 32

Solution

The orbiting electron forms a current loop, and the magnetic field it produces at the nucleus is

B = \frac{μ _{0} I}{2 r}

with

I = \frac{e v}{2 π r}

, hence

B = \frac{μ _{0} e v}{4 π r ^{2}} \propto \frac{v}{r ^{2}}

. In the Bohr model

v \propto \frac{1}{n}

and

r \propto n^{2}

, so

B \propto \frac{1/ n}{n ^{4}} = \frac{1}{n ^{5}}

. The ratio for the

2^{nd}

and

4^{th}

orbits is therefore

\frac{B _{2}}{B _{4}} = (\frac{4}{2})^{5} = 2^{5} = 32

JEE Main · 2026 · 02 Apr 2026 · Shift 2 · Integer answer

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