PYQ NEET- Moving Charges And Magnetism L-6

Question: An electron moving in a circular orbit of radius $r$ makes $n$ rotations per second. The magnetic field produced at the centre has magnitude#

A) $\frac{\mu_0 n^2 e}{r}$

B) $\frac{\mu_0 n e}{2 \tau}$

C) $\frac{\mu_0 n e}{2 \pi r}$

D) Zero

Answer: (B) $\frac{\mu_0 n e}{2 \tau}$#

Sol:#

Current in the orbit, $I=\frac{e}{T}$ $$ \begin{alignedat} & I=\frac{e}{(2 \pi / \omega)}=\frac{\omega e}{2 \pi} \ & =\frac{(2 \pi n) e}{2 \pi}=n e \end{aligned} $$

Magnetic field at centre of current carrying circular coil is given by $$ B=\frac{\mu_0 I}{2 r}=\frac{\mu_0 n I}{2 r} $$