(a) Write the expression for the magnetic force acting on a charged particle moving with velocity v in the presence of magnetic field B

(a) Write the expression for the magnetic force acting on a charged particle moving with velocity v in the presence of magnetic field B.
(b) A neutron, an electron and an alpha particle moving with equal velocities, enter a uniform magnetic field going into the plane of the paper as shown. Trace their paths in the field and justify your answer.

(a)
The magnitude of force is given by,
Fm = Bqv sin$\theta $

Alpha-particle will trace circular path in anti-clockwise sense as its deviation will be in direction of (vxB).
Neutron will pass without any deviation as magnetic field does not exert force on neutral particle.
Electron will, trace circular path in clockwise sense as its deviation will be in the direction*opposite to (v X B) with a smaller radius due to larger charge/ mass ratio as r =mv/qb