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. $\frac{{\mu }_o{n}^{2}e}{r}$
• B. $\frac{{\mu }_{o}ne}{2r}$
• C. $\frac{{\mu }_{o}ne}{2\pi r}$
• D. Zero

Answer 1

The correct option is B $\frac{{\mu }_{o}ne}{2r}$

Magnetic field at center of circular coil is given as $\overrightarrow{B}=\frac{{\mu }_{\circ }I}{2r}$ where I is current in coil.
time taken in n revolution is 1 sec, time taken in 1 rev$=\frac{1}{n}$
$I=\frac{q}{t}=\frac{e}{\frac{1}{n}}$
$\overrightarrow{B}=\frac{{\mu }_{\circ }ne}{2r}$
hence, correct answer is option B.