The ratios of the masses and charges of a proton and an alpha particle are respectiely `1:4 and 1:2`. They enter a uniform magnetic field of magnitude B normally with same velocity. What will be the ratio of the radii of the circular paths described by the particles in each case ?

Explanation

Radius of the circular path `r=(mv)/(qB),B` = constant.
If the velocity is the same then, `r prop (m)/(q)`,
i.e., `(r_(1))/(r_(2))=(m_(1))/(m_(2))xx(q_(1))/(q_(2))=(1)/(4)xx(2)/(1)=(1)/(2)`