Respuesta :
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.
