First slide

Motion of a charged particle

Question

An electron having kinetic energy K is moving in a circular orbit of radius R perpendicular to a uniform magnetic induction B. If kinetic energy is doubled and magnetic induction tripled, the radius will be

Moderate

A

$\frac{3 R}{2}$
B

$\sqrt{\frac{3}{2}} R$
C

$\sqrt{\frac{2}{9}} R$
D

$\sqrt{\frac{4}{3}} R$

Solution

$R a d i u s o f c i r c l e = R = \frac{m V}{B q} = \frac{\sqrt{2 m K}}{B q} N e w r a d i u s = R^{1} = \frac{\sqrt{2 m (2 K)}}{(3 B) q} = \sqrt{\frac{2}{9}} \frac{\sqrt{2 m K}}{B q} = \sqrt{\frac{2}{9}} R$

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