A charged particle isinjected into a uniform magnetic field such that its velocity vector is perpendicular to themagnetic field vector. Ignoring the particle's weight, the particlewillA) follow a spiralpath. B) move in a straight line. C) move along a parabolic path. D) follow a circular path.

The correct option is D

A charged particle is injected into a uniform magnetic field such that its velocity vector is perpendicular to the magnetic field vector follows a circular path.

Explanation:

A charged particle can move in a circular path due to magnetic force. We know that magnetic force does not do any work on the charged particle since the magnetic force is perpendicular to the velocity. The velocity is constant in magnitude but its direction of motion changes which results in circular motion. The magnetic force and the centripetal force are related as

F = Fc

qvB = mv²r

r = mv/qB

Here r is the radius of charged particle's path, v is the velocity, B is the magnetic field and q and m are charge and mass of the charged particle respectively.

D) follows a circular path

Explanation:

This is because the magnetic force F on the charge, q due to the magnetic field B with velocity vector v perpendicular to it, equals the centripetal force acting on the charge.

So, F = Bqv = mv²/r.

So it follows a circular path.