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
\([\mu_0 \rightarrow \text {permeability of free space, } m \rightarrow\) \(\text {mass of electron} \ \varepsilon_0 \rightarrow \text {permittivity of free space, }\) \(h \rightarrow \text {Planck's constant}]\)

To keep the electron in its orbit, the centripetal force on the electron must be equal to the electrostatic force of attraction,
\(\frac{m v^2}{r}=\frac{1}{4 \pi \varepsilon_0} \frac{e^2}{r^2}\quad---(1)\)
According to Bohr's angular momentum quantization condition:
\(\Rightarrow \pi r m e^2=\varepsilon_0 h^2\)
\(r=\frac{\varepsilon_0 h^2}{\pi m e^2} \quad---(3)\)
From (ii) and (iii), we have
\(v=\frac{h \pi m e^2}{2 \pi m \varepsilon_0 h^2}=\frac{e^2}{2 \varepsilon_0 h}\)
The magnetic field at the center of the circular loop is given by,
\(B=\frac{\mu_0 I}{2 r}\)
where, current \(I=\frac{\mathrm{q}}{\mathrm{T}}\) and time \(T=\frac{2 \pi r}{v}\)
\(\therefore I=\frac{e v}{2 \pi r}\)
\(\Rightarrow\text B=\frac{\mu_{0}\text{ev}}{4\pi\text{r}2}\quad---(4)\)
Using, equations (2), (3) and (4) we have,
\(B=\frac{\mu_0 e^7 \pi m^2}{8 \varepsilon_0^3 h^5}\)