Question

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. $\sqrt{\frac{B}{v}}$

Answer 1

Answer: (C)

$\sqrt{\frac{v}{B}}$

Answer 2

The time period of electron moving in a circular orbit
$T=\frac{\text { circumference of circular path }}{\text { speed }}$
$=\frac{2 \pi r}{v}$
and equivalent current due to electron flow
$I=\frac{e}{T}=\frac{e}{(2 \pi r / v)}=\frac{e v}{2 \pi r}$
Magnetic field at centre of circle
$B=\frac{\mu_{0} I}{2 r}=\frac{\mu_{0} e v}{4 \pi r^{2}}$
$\Rightarrow r \propto \sqrt{\frac{v}{B}}$