Chapter 26, Problem 1FTD

A charged particle moves through a region containing only a magnetic field. Under what condition will it experience no force?

To determine

The condition when an electron will not experience a force in a magnetic field.

Answer to Problem 1FTD

An electron will not experience any force in a magnetic field when the particle is moving either parallel or antiparallel to the direction of field.

Explanation of Solution

Write the equation to find the force acting on a particle in magnetic field.

$F=qvB\sin \theta$

Here,

$F$ is the force

$q$ is the charge

$v$ is the velocity

$B$ is the magnetic field

The force becomes zero when the sine term becomes zero. For sine term to be zero the angle $\theta$ must be $0°\text{or}\text{180}°$.

Therefore the force acting on a particle becomes zero only when the particle is moving parallel or antiparallel to the direction of magnetic field.

Conclusion:

Therefore, an electron will not experience any force in a magnetic field when the particle is moving either parallel or antiparallel to the direction of field.