Question

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

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

Answer 1

Answer: (B)

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

The radius of a circular orbit in the presence of magnetic filed B is

$R=\frac{\sqrt{2Km}}{Bq}$

or $R\propto \frac{\sqrt{K}}{B}$

so, $\frac{r}{R}=\frac{\sqrt{2K}}{3B}\times \frac{\sqrt{B}}{K}$

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