question_answer

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) Zero

B) \[\frac{{{\mu }_{0}}{{n}^{2}}e}{r}\]

C) \[\frac{{{\mu }_{0}}ne}{2r}\]

D) \[\frac{{{\mu }_{0}}ne}{2\pi r}\]

Correct Answer: C

Solution :

[c] Radius of circular orbit = r No. of rotations per second = n i.e., \[T=\frac{1}{n}\] Magnetic field at its centre, \[{{B}_{c}}=?\] As we know, current \[i=\frac{e}{T}=\frac{e}{(1/n)}=en=\] equivalent current Magnetic field at the centre of circular orbit, \[{{B}_{c}}=\frac{{{\mu }_{0}}i}{2r}=\frac{{{\mu }_{0}}ne}{2r}.\]