Question

A charged particle is moving in a uniform magnetic field in a circular path of radius 'R'. When the kinetic energy of the particle is increased to three times, then the new radius will be

• A. $\frac{R}{3}$
• B. $\frac{R}{\sqrt{3}}$
• C. $\sqrt{3} \cdot R$
• D. $3 \cdot R$

Answer 1

Answer: (C)

$\sqrt{3} \cdot R$

Answer 2

For a charged particle in a magnetic field, the radius of its circular path is given by

$$r = \frac{\sqrt{2mK}}{qB}$$

This shows that $r \propto \sqrt{K}$. When the kinetic energy is tripled (i.e., $K' = 3K$), the new radius $R'$ becomes

$$R' = R \sqrt{3}$$