Question

A proton and an alpha particle having the same kinetic energy are allowed to pass through a uniform magnetic field perpendicular to the direction of their motion. Compare the radii of the paths of proton and alpha particle.

Answer 1

a proton has a mass= m & charge = q

mass of an alpha particlem' = 4m & charge q' = 2q

K.e of proton = K.e of alpha particle

$0.5m{v}^2=0.5m^{\prime }{v^{\prime }}^2$

$v^2=4{v^{\prime }}^2$

$\frac{v}{v^{\prime }}=\sqrt{4}=2$

radius of charged particle in uniform magnetic field is $r=\frac{mv}{qB}$

$\frac{r}{r^{\prime }}=\frac{m}{m^{\prime }}\times \frac{v}{v^{\prime }}\times \frac{q^{\prime }}{q}=\frac{1}{4}\times \frac{2}{1}\times \frac{2q}{q}=\frac{1}{1}$