# 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

B) move in a straight line.
C) move along a parabolic path.

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

1. 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:

$$F=q v B \sin \theta$$

where

q is the charge

v is the velocity of the particle

B is the magnetic field

$$\theta$$ is the angle

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

$$\theta$$ = $$90^{\circ}$$ and sin$$\boldsymbol{\theta}$$ =sin 90 degree = 1.

So applying the formula,

the force is simply $$F=q v B$$

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.