Question

When a proton moves in a uniform magnetic field, the momentum change but its kinetic energy does not change because:
(A) The magnetic force exerted will be perpendicular to the direction of motion of the proton.
(B) Work done will be zero.
(C) Kinetic energy does not change.
(D) All

Answer 1

Kinetic energy depends on the work done by the force on the proton. The work done is zero when the force is perpendicular to the displacement.

Complete step by step answer:
A proton of charge q and mass m moves in XY plane and a uniform magnetic field B is acting along the Z axis. The velocity of the particle be v. So, the magnetic Lorentz force on the proton will be given by the formula F= q(v×B) . Thus, the force F is perpendicular to the plane containing v and B and so the force acts perpendicular to the velocity of proton.As the magnetic force is perpendicular to the direction of motion of the proton, so the force does no work i.e. the work done is zero. The magnitude of velocity i.e., speed remains the same and only its direction changes. So, the velocity changes and hence the momentum also gets changed. Thus, the kinetic energy does not change.
Hence,option (B) is correct.

Note: In a circular path, work done is zero as the angle between force and displacement is 90⁰[W = FS cos 90⁰=0 since cos 90⁰ is 0]. The kinetic energy is defined as the energy possessed by a body due to virtue of its motion. In this case, the kinetic energy remains constant as the amount of work done is zero.