Question

A charged particle is moving in a uniform magnetic field in a circular path. The energy of the particle is doubled. If the initial radius of the circular path was R, the radius of the new circular path after the energy is doubled will be :

• A. $0.5R$
• B. $\sqrt{2}R$
• C. $2R$
• D. $\frac{R}{\sqrt{2}}$

Answer 1

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

The radius of the changed particle moving in the magnetic field $=\frac{mv}{Bq}$
$R=\frac{mv}{Bq}$-------(1)
As energy of particle is doubled, kinetic energy is doubled,
New velocity $V_1$,
$\frac{1}{2}mv{{}_1}^2=m{v}^2$
$\to v_1=\sqrt{2}v$
So,
New $R$ $=\frac{mv}{Bq}\sqrt{2}$
New $R=\sqrt{2}R$ [ from (1) ]