For a particle of mass m and charge q moving in a circular path in a magnetic field B, find how does its kinetic energy depend on the radius of the curvature of its path r.

(A) kinetic energy of a particle is proportional to 1/r.
(B) kinetic energy of a particle is proportional to r^2
(C) kinetic energy of a particle is proportional to 1/r^2.
(D) kinetic energy of a particle is proportional to r.

B) K.E is proportional to r²

Explanation:

The motion of particle  in magnetic field is caused by lorentz force.

F=qvB--(1)

v= Velocity of particle

q=magnitude of charge

B=Strength of magnetic field

To move the object in circular path, centripetal force is

Which must be equal to lorentz force. So equating (1) and(2)

K.E is given as:

Substituting values of v from (3) in above:

Which shows K.E is directly proportional to r^2

number of electrons for neutral cl