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# A charged particle isinjected into a uniform magnetic field such that its velocityvector is perpendicular to themagnetic field vector. Ignor

Question

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.

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1 year
2021-09-04T01:31:11+00:00
2021-09-04T01:31:11+00:00 1 Answers
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## Answers ( )

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:[tex]F=q v B \sin \theta[/tex]

where

q is the charge

v is the velocity of the particle

B is the magnetic field

[tex]\theta[/tex] is the angle

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

[tex]\theta[/tex] = [tex]90^{\circ}[/tex] and sin[tex]\boldsymbol{\theta}[/tex] =sin 90 degree = 1.

So applying the formula,

the force is simply [tex]F=q v B[/tex]

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.