8.

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 paper, as shown. Trace their paths in the field and justify your answer. 

a) 

Force acting on a charged particle q, which is moving with velocity v in a magnetic field B, is given by, 


                                          
The right-hand rule gives the direction of this force. The direction of the force is perpendicular to the plane containing velocity v and magnetic field B. 

b) 

A charged particle experiences a force when it enters the magnetic field. Due to the presence of magnetic field, the charged particle will move in a circular path. This is because the force is perpendicular to the velocity of the charged particle. 

Radius of the circular path in which the charged particle is moving is given by, 


 

Since the neutron has no charge, it will move along a straight line. 

The electron will follow a circular path which has a radius smaller than that of the alpha particle. This is because the mass to charge ratio of the alpha particle is more than that of the electron. 

Therefore, the electron will move in the clockwise direction and the electron will move in the anticlockwise direction as per the Right Hand Rule.