An electron revolves in a circular orbit of radius r with angular...

Magnetic field at the centre of circular loop.

$B = \dfrac{{μ}_{0}l}{2r}... \left(i\right)$

Period of revolution of electron, where $\omega =$ angular velocity of electron

$T = \dfrac{2\pi}{ω}$

where, $\omega =$ angular velocity of electron.

Current produced due to movement of electron,

$I = \dfrac{e}{T} = \dfrac{e}{2\pi\omega} = \dfrac{e\omega}{2\pi}$

On substituting the value of $I$ in Eq. (i), we get

$B = \dfrac{\mu0}{2r} \cdot \dfrac{e\omega}{2\pi}$

$⇒ B = \dfrac{{μ}_{0}e\omega}{4\pir}$