Question

In which cases does a charged particle not experience a force in a magnetic field?

Hint:

The magnetic force on a charged particle is given by the cross product of its velocity and the magnetic field. Therefore, the particle will not experience any force if its velocity is parallel to the magnetic field, or if the velocity is zero.

Answer 1

A charged particle experiences a force in a magnetic field according to the Lorentz force law: \[ \vec{F} = q (\vec{v} \times \vec{B}) \] where: - \( \vec{F} \) is the force on the particle, - \( q \) is the charge of the particle, - \( \vec{v} \) is the velocity of the particle, - \( \vec{B} \) is the magnetic field. From this equation, we can conclude that the charged particle will not experience a force in the following cases: 1. When the velocity of the particle is parallel to the magnetic field: If the velocity of the charged particle is parallel or anti-parallel to the magnetic field (\( \vec{v} \parallel \vec{B} \) or \( \vec{v} = k \vec{B} \) where \( k \) is a constant), then the cross product \( \vec{v} \times \vec{B} \) will be zero, and therefore, the particle will not experience any force. 2. When the velocity of the particle is zero: If the charged particle is at rest (\( \vec{v} = 0 \)), then no force will act on it, as the magnetic force depends on the velocity of the particle. Thus, a charged particle does not experience a force in a magnetic field if: - The particle is at rest, or - The particle’s velocity is parallel (or anti-parallel) to the magnetic field.