Question

A charged particle enters into a uniform magnetic field such that its velocity vector is perpendicular to the magnetic field vector. Ignoring the particle's weight, what type of path will the particle follow?
A) follow a spiralpath.
B) move in a straight line.C) move along a parabolic path.
D)follow a circular path.

Answer 1

Answer:

The particle path will follow

(d) a circular path

Explanation:

When a charged particle having charge of magnitude '$q$' enters into a magnetic field such that its velocity vector '$\vec{V}$' is perpendicular to the direction of the magnetic field '$\vec{B}$', then it will experience a force, called Lorentz force ($\vec{F_{L}}$), given by

$\vec{F_{L}} = \vec{V} \times \vec{B}$

As shown in the figure, the magnetic field is directed perpendicular to the plane and towards the plane (as shown by the circle and 'X'-sign) and the velocity vector is from left to right on the plane.

According to the property of cross-product, the Lorentz force ($F_{L}$) acting on the particle will be perpendicular to the instantaneous position of the particle, making the path of the particle to be a circular path,as shown in the figure.