Physics - Magnetism Question with Solution | TestHub

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 $I=\frac{e}{T}=\frac{e}{(2\pi r/v)}=\frac{ev}{2\pi r}$ Magnetic field at centre of circle $B=\frac{{\mu }_{0}I}{2r}=\frac{{\mu }_{0}ev}{4\pi r^2}$ $\Rightarrow r\propto \sqrt{\frac{v}{B}}$