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
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${\text{B}} = \frac{{{\mu _0}{\text{I}}}}{{2{\text{R}}}} = \frac{{{\mu _0}}}{{2{\text{R}}}}\left( {\frac{{\text{e}}}{{\text{T}}}} \right) = \frac{{{\mu _0}}}{{2{\text{R}}}}\left( {\frac{{{\text{ev}}}}{{2\pi {\text{R}}}}} \right)$
$ \Rightarrow {{\text{R}}^2} = \frac{{{\mu _0}{\text{ev}}}}{{4\pi {\text{B}}}} \Rightarrow {\text{R}} \propto \sqrt {\frac{{\text{v}}}{{\text{B}}}} $
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