The force on a particle of charge and velocity making and angle with magnetic field is given by:
The magnitude of the force when the magnetic field is normal to velocity is given by:
As the force is perpendicular to the velocity, (resultant of cross product), it can only change the direction and not the speed of the particle. Hence, it will move in a circle. Let r be the radius of this circular path. The centripetal force is given by:
Equating (1) and (2) , we get
We know that the kinetic energy is given by:
Substituting in (3), we have
The ratio of mass of alpha particle to the mass of proton is 4:1.
The ratio of the charge on alpha particle to the charge on proton is 2:1.
Taking the ration of the radii, we have
The ratio of the radii of is 1.
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