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  4. If velocity of a charged particle is doubled and strength of magnetic field is halved, then radius becomes :

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Q. If velocity of a charged particle is doubled and strength of magnetic field is halved, then radius becomes :

Rajasthan PMTRajasthan PMT 2006Moving Charges and Magnetism

Solution:

Force $=q v B=\frac{m v^{2}}{r}=($ centripetal force)
$\Rightarrow r=\frac{m v}{q B}$
$\therefore r^{\prime}=\frac{m \times 2 v}{q \times \frac{B}{2}}=4 r$