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                                                                                                          [NEET  2015]                        

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

B)       zero     

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

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

Correct Answer: D

Solution :

[d] As \[I=\frac{q}{t}\]

So, for an electron revolving in a circular orbit of radius r

\[q=e\] and \[t=T\]

\[\Rightarrow \]   \[I=\frac{e}{T}=\frac{e}{2\pi /\omega }=\frac{\omega e}{2\pi }=\frac{2\pi ne}{2\pi }=ne\]

The magnetic field produced at the centre is

\[B=\frac{{{\mu }_{0}}I}{2R}=\frac{{{\mu }_{0}}ne}{2r}\]