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

B)  zero     

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

D)  \[\frac{{{\mu }_{0}}ne}{2r}\]

Correct Answer: D

Solution :

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