An `alpha`- particle and a proton of the same kinetic energy are in turn allowed to pass through a magnetic field `vecB`, acting normal to the direction of motion of the particles. Calculate the ratio of radii of the circular paths described by them.

Explanation

We know that radius of circular path `r = (mv)/(qB) = (sqrt(2mk))/(qB)`
Here `K_(alpha) = K_(p)` but `m_(alpha) = 4m and q_(alpha) = 2q_p`
`:. (r_(alpha))/(r_p) = sqrt((m_(alpha))/(m_p)) xx ((q_P)/(q_(alpha))) = sqrt((4m_p)/(q_(alpha))) xx ((q_p)/(2q_p)) = 1`
`implies r_(alpha) = r_(p)`