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 become:

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

Answer 1

The correct option is C $\sqrt{\frac{2}{9}}R$

Given,

$KE=TJule$

$Radius=R$

$MagneticInduction=\overrightarrow{B}$

Then , the radius

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

when,

$KE=2T$

$B=3\overrightarrow{B}$

$Radius=r^{\prime }$

When,

$r^{\prime }=\frac{\sqrt{2m\left(2T\right)}}{q\left(3B\right)}$

$r^{\prime }=\sqrt{2}\frac{\sqrt{2mT}}{3qB}$

$r^{\prime }=\frac{\sqrt{2}}{3}\frac{\sqrt{2mT}}{qB}$

$r^{\prime }=\frac{\sqrt{2}}{3}R$

Therefore, the radius will be $\sqrt{\frac{2}{9}}R$