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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Kim Chi 1 year 2021-09-04T01:31:11+00:00 1 Answers 0 views 0

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    2021-09-04T01:32:55+00:00

    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 D

    Explanation:

    Magnetic force causes charged particles to move in spiral paths. The Particle accelerators keep the protons to follow circular paths when it is in the magnetic field. Velocity has a change in direction but magnitude remains the same when this condition exists.

    The magnetic force exerted 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 perpendicular to both B and v and so according to the right-hand rule, we have:

    • a force that is always perpendicular to the velocity, v
    • a force which is constant in magnitude (because the magnitude of v or B does not change)

    This means that the force acts as a centripetal force, so it will keep the charged particle in a uniform circular motion.

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