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 is subject to a force in a magnetic field as described by the Lorentz force law: \[ \vec{F} = q (\vec{v} \times \vec{B}) \] where: - \( \vec{F} \) represents the force exerted on the particle, - \( q \) denotes the particle's charge, - \( \vec{v} \) is the particle's velocity, - \( \vec{B} \) signifies the magnetic field. Based on this equation, a charged particle will experience no force under the following conditions: 1. Velocity parallel to the magnetic field: When the particle's velocity is parallel or anti-parallel to the magnetic field (\( \vec{v} \parallel \vec{B} \) or \( \vec{v} = k \vec{B} \), where \( k \) is a scalar constant), the cross product \( \vec{v} \times \vec{B} \) becomes zero. Consequently, no force will be exerted on the particle. 2. Zero velocity: If the charged particle is stationary (\( \vec{v} = 0 \)), no magnetic force will act upon it, as the force is contingent on the particle's velocity. In summary, a charged particle experiences no force in a magnetic field when either: - The particle is at rest, or - The particle's velocity vector is aligned (parallel or anti-parallel) with the magnetic field vector.