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

The time period of electron moving in a circular orbit

$$\begin{gathered} \text{T}=\frac{\text{circumference\hspace{0.17em}of\hspace{0.17em}circular\hspace{0.17em}path}}{\text{speed}}=\frac{2\pi \text{r}}{\text{v}} \\ Electric current corresponds to the revolution of electron is \\ I=\frac{\text{e}}{\text{T}}=\frac{\text{e}}{\left(2\pi \text{r/v}\right)}=\frac{\text{ev}}{2\pi \text{r}} \\ Magnetic field at centre of circle \text{B}=\frac{{\mu }_{0}I}{2\text{r}}=\frac{{\mu }_0\text{ev}}{4\pi {\text{r}}^{\text{2}}} \\ Hence\text{r}=\sqrt{\frac{{\mu }_0}{4\pi }.\frac{\text{ev}}{\text{B}}}\Rightarrow \text{r}\propto \sqrt{\frac{\text{v}}{\text{B}}} \end{gathered}$$