Question

A charged particle is moving in a uniform magnetic field in a circular path of radius R. When energy of the particle is doubled, then the new radius will be :

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

Answer 1

Answer: (B)

Energy of charged particle revolving in a magnetic field, $E=\frac{1}{2}m{\upsilon }^2$ But $\frac{m{\upsilon }^2}{R}=q\upsilon B$ $\Rightarrow$ $\upsilon =\frac{qBR}{m}$ $\therefore$ $E=\frac{1}{2}m\frac{q^2{B}^2{R}^2}{m^2}$ $=\frac{q^2{B}^2{R}^2}{2m}$ $\Rightarrow$ $E\propto R^2$ $\Rightarrow$ $R\propto \sqrt{E}$ If R' is new radius $\frac{R^{\prime }}{R}=\sqrt{\frac{E^{\prime }}{E}}$ $\Rightarrow$ $\frac{R^{\prime }}{R}=\sqrt{2}$ $\Rightarrow$ $R^{\prime }=\sqrt{2}R$