Question

A magnetic field exerts a force on a charged particle:

a. never

b. if the particle is moving across the field lines

c. if the particle is moving along the field lines

c. if the particle is at rest.

Answer 1

Concepts and reason

The concepts used to solve this question are magnetic field and force exerted on a charged particle in the magnetic field.

First, write the equation for the force exerted on a moving charged particle in the magnetic field and then define the angle made by the charged particle with the magnetic field lines.

Later determine or check the force exerts on a charged particle in the possible conditions to find the correct answer choice.

Fundamentals

Magnetic field:

The magnetic field is defined as a region around a magnet (magnetic material) or moving electric charge within which the force of magnetism acts.

Force on a charged particle in a magnetic field:

When a charged particle is moving in a magnetic field then there is a force due to magnetic field exerts on the charged particle called magnetic force.

Mathematically, the expression for the force exerted on a moving charged particle in the magnetic field is,

$F = qvB\sin \theta$

Here, $q$ is a charge on the charged particle, $v$ is the speed of the charged particle, $B$ is a magnetic field and $\theta$ is the angle between the speed vector of the charged particle and the magnetic field lines.

The expression for the force exerted on a moving charged particle in the magnetic field is,

$F = qvB\sin \theta$

When a charged particle moves in the magnetic field then the charged particle experiences a force. The force experienced by the moving charged particle depends on the intensity of the magnetic field, the direction of magnetic field lines and the velocity vector of the charge, and the speed of the charged particle.

When the charged particle moves along the magnetic field lines, then the angle between the magnetic field lines and speed of the charged particle become $0^\circ$ .

When the charged particle moves across the magnetic field lines, then the angle between the magnetic field lines and speed of the charged particle become $90^\circ$ .

The force exerts on a moving charged in the magnetic field.

$F = qvB\sin \theta$

Substitute $90^\circ$ for $\theta$ in above expression.

$\begin{array}{c}\\F = qvB\sin 90^\circ \\\\ = qvB\\\end{array}$

Substitute $0^\circ$ for $\theta$ in above expression.

$\begin{array}{c}\\F = qvB\sin 0^\circ \\\\ = 0\\\end{array}$

If the charged particle is at rest than the speed of the charged particle becomes zero which results in zero magnetic force on the charged particle.

Ans:

If the particle is moving across the field lines.