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
AIPMT 2005, Medium
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(c) Electric current corresponds to the revolution of electron is $i = \frac{{ev}}{{2\pi r}}$
Magnetic field due to circular current at the centre $B = \frac{{{\mu _0}}}{{4\pi }}.\frac{{2\pi \,i}}{r} = \frac{{{\mu _0}}}{{4\pi }}.\frac{{ev}}{{{r^2}}}$==> $r = \sqrt {\frac{{{\mu _0}}}{{4\pi }}.\frac{{ev}}{B}} $==> $r \propto \sqrt {\frac{v}{B}} $.
Magnetic field due to circular current at the centre $B = \frac{{{\mu _0}}}{{4\pi }}.\frac{{2\pi \,i}}{r} = \frac{{{\mu _0}}}{{4\pi }}.\frac{{ev}}{{{r^2}}}$==> $r = \sqrt {\frac{{{\mu _0}}}{{4\pi }}.\frac{{ev}}{B}} $==> $r \propto \sqrt {\frac{v}{B}} $.
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