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  4. 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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Q. 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

AIPMTAIPMT 2005Moving Charges and Magnetism

Solution:

The magnetic field produce by moving electron
in circular path $B = \frac{{\mu}_0 i }{2r}$
image
Where $i=\frac{q}{t}=\frac{q}{2 \pi r} \times v$
$\therefore=\frac{\mu_{0} q v}{4 \pi r^{2}} $
$\Rightarrow B=\sqrt{v / B}$