# A particle and a

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

Now,

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.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses