Question

An electron having kinetic energy T is moving in a circular orbit of radius R perpendicular to a uniform magnetic induction $\overrightarrow{B}$ If kinetic energy is doubled and magnetic induction tripled, the radius will

• A. $\frac{3R}{2}$
• B. $\frac{\sqrt{2}}{3}R$
• C. $\sqrt{\frac{2}{9}}R$
• D. $\sqrt{\frac{4}{3}}R$

Answer 1

The correct option is B $\frac{\sqrt{2}}{3}R$

We know$,$

$R=\frac{\sqrt{2mk}}{qB}$

$R^{\prime }=\frac{\sqrt{2m2k}}{q\left(3B\right)}$

$=\frac{\sqrt{2}}{3}\frac{\sqrt{2mk}}{qB}$

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

Hence,

option $\left(B\right)$ is correct answer.