A charge ‘q’ moving along the -X-axis with a velocity $\vec{v}$ is subjcted to a uniform magnetic field B acting along the Z-axis as it crosses the origin O.

(i) Trace its trajectory.
(ii) Does the charge gain kinetic energy as it enters the magnetic field? Justify your answer.

Solution

Given,

(i) As the charged particle is moving along negative x axis subjected to uniform magnetic field along Z axis it will experience a force when it crosses the origin F=q (

\overset{⇀}{v} \times \overset{⇀}{B}

).
The trajectory of charged particle q moving along (-)ve X-axis will be helical.

(ii) The force which is acting on the charged particle due to it's magnetic field is always perpendicular to the velocity at each point. Therefore, the field does no work done on a moving charged particle. Hence, it will not gain any kinetic energy. Moreover, magnitude of velocity does not change. Only, the direction of velocity changes for the charged particle.