Question

A proton and an alpha particle of the same velocity enter in turn a region of uniform magnetic field acting in a plane perpendicular to the magnetic field. Deduce the ratio of the radii of the circular paths described by the particles. Explain why kinetic energy of the particle after emerging from the magnetic field remains unaltered.

Answer 1

For proton:

q_p = q; r_p = ?; m_p = m and 

For α-particle:

q_α = 2q; r_α = ?; m_α = 4m

1 = \(\frac{r_a}{2r_p}\)

or r_α = 2 r_p

K.E. of the particle remains the same since the angle between centripetal force and direction of motion is 90°. No work is done in rotation of the particle since W = FS cos 90° = 0. Hence K.E. remains constant.