Assuming the atom is in the ground state, the expression for the magnetic field at a point nucleus in hydrogen atom due to circular motion of electron is \(\left[\mu_0=\right.\) permeability of free space, \(m\) \(=\) mass of electron, \(\in_0=\) permittivity of free space, \(\mathrm{h}=\) Planck's constant]

The magnetic field at the center of a circular coil is given by
\(
\mathrm{B}=\frac{\mu_0 \mathrm{I}}{2 \mathrm{r}}
\)
If \(\mathrm{T}\) is the periodic time of revolving electron, then \(\mathrm{I}=\frac{\mathrm{e}}{\mathrm{T}}\)
Also, \(\mathrm{T}=\frac{2 \pi \mathrm{r}}{\mathrm{V}}\)
\(
\therefore \mathrm{I}=\frac{\mathrm{eV}}{2 \pi \mathrm{r}}
\)
\(
\therefore \mathrm{B}=\frac{\mu_0 \mathrm{eV}}{4 \pi \mathrm{r}^2}
\)
For electron in ground state,
\(
\mathrm{V}=\frac{\mathrm{e}^2}{2 \in_0 \mathrm{~h}} \text { and } \mathrm{r}=\frac{\mathrm{h}^2 \in_0}{\pi \mathrm{m}^2}
\)
Putting these values in eq.(1) and simplifying we get
\(
\therefore \mathrm{B}=\frac{\mu_0 \mathrm{e}^7 \pi \mathrm{m}^2}{8 \epsilon_0^3 \mathrm{~h}^5}
\)