Question

Write the expression, in a vector form, for the Lorentz magnetic force $F$ due to a charge moving with velocity $v$ in a magnetic field \[B\]. What is the direction of the magnetic force?

Answer 1

Hint: The Lorentz force can be determined by the formula, \[F = qv \times B\] where $q$ is the charge, $v$ is the velocity and $B$ is the magnetic field density. The right hand thumb rule is applicable in determining the Lorentz force.

Complete answer:
Let us start by examining Lorentz magnetic force. Lorentz force,
We know, the force experienced by a charged particle moving in a space where both an electronic and magnetic field exists, that force is called the Lorentz force.
The Lorentz magnetic force will be equal to, \[\overrightarrow F = q(\overrightarrow v \times \overrightarrow B )\]
Where, $q$ is the charge of the particle.
That is, the force vector, $\overrightarrow F $ will be equal to the cross product of $\overrightarrow v $ and $\overrightarrow B $ is multiplied with the charge of the particle.
From the above equation, it is understood that the direction of force is equal to the direction of cross product of velocity vector $\overrightarrow v $ and magnetic field vector, $\overrightarrow B $.
That means it is perpendicular to the plane containing velocity vector $\overrightarrow v $ and magnetic field vector, $\overrightarrow B$.
Lorentz force is Perpendicular to both magnetic field and velocity. Lorentz force is only a definition in principle because a real particle can alter the electromagnetic field that the particle experiences, because of the self-generated electrical and magnetic field. In Addition. If the particle is gaining acceleration as it moves in a curved path it may emit radiation and causes the loss in its kinetic energy.

Note: The Lorentz force is used in electromagnetism. It occurs in a magnetic field, when a charge moves through it. Lorentz force is Perpendicular to both magnetic field and velocity. In real materials. However, the Lorentz force is inadequate to describe the collective behaviour of charged particles.