A charged particle isinjected into a uniform magnetic field such that its velocityvector is perpendicular to themagnetic field vector. Ignoring the particle’s weight, the particlewill

A) follow a spiralpath.

B) move in a straight line.

C) move along a parabolic path.

D)follow a circular path.

A charged particle is injected into a uniform magnetic field such that its velocity vector is perpendicular to the magnetic field vector. Ignoring the particle’s weight, the particle will

follow a circular path.Option DExplanation:Magnetic forcecauses charged particles to move inspiralpaths. TheParticle acceleratorskeep the protons to followcircular pathswhen it is in the magnetic field.Velocity has a change in direction but magnitude remains the samewhen this condition exists.The

magnetic forceexerted on the charged particle is given by the formula:where

q is the charge

v is the velocity of the particle

B is the magnetic field

is the angle

In this problem, the velocity is perpendicular to the magnetic field vector, hence

= and sin =sin 90 degree = 1.

So applying the formula,

the force is simply

Also, the force is

perpendicularto both B and v and so according to the right-hand rule, we have:This means that the force acts as a centripetal force, so it will keep the charged particle in a uniform

circularmotion.