Q. An electron moves in a circular orbit with a uniform speed $v.$ It produces a magnetic field $B$ at the centre of the circle. The radius of the circle is proportional to
A) $\frac{B}{v}$
B) $\frac{v}{B}$
C) $\sqrt{\frac{v}{B}}$
D) $\sqrt{\frac{B}{v}}$
Explanation
(c) The time period of electron moving in a circular orbit
$T = \frac{circumference\ of\ cirular\ path}{speed} = \frac{2\pi r}{v}$
And equivalent current due to electron flow
$I = \frac{e}{T} = \frac{e}{(2\pi r/v)\ } = \frac{ev}{2\pi r}$
Magnetic field at centre of circle
$B = \frac{\mu_{0}I}{2r} = \frac{\mu_{0}ev}{4\pi r^{2}} \Rightarrow r \propto \sqrt{\frac{v}{B}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.