Can a Charged Particle Move in a Straight Line in a Nonzero Magnetic Field?

[Rsealey]

Homework Statement

A charged particle moves in a straight line through a particular region of space. Could there be a nonzero magnetic field in this region? In either case, include a sketch as well as prose in your justification.

Homework Equations

The Attempt at a Solution

The force that a magnetic field exerts on a charged particle moving through it is given by F=qvB, sin theta = qvB where B is the component of the field perpendicular to the particle’s velocity. Since the particle moves in a straight line the magnetic force must be zero.

 

[Doc Al]

The force that a magnetic field exerts on a charged particle moving through it is given by F=qvB, sin theta = qvB where B is the component of the field perpendicular to the particle’s velocity.

OK.

Since the particle moves in a straight line the magnetic force must be zero.

The magnetic force is zero. What about the field?

 

[BiGyElLoWhAt]

The force that a magnetic field exerts on a charged particle moving through it is given by $F=qvB$ $sin (\theta )$[/color] $= qvB$ where $B$ is the component of the field perpendicular to the particle’s velocity[/color]. Since the particle moves in a straight line the magnetic force must be zero.

Hmmm...
Another way to look at that relationship is $\vec{F}=q\vec{v}\times \vec{B}$
It's essentially the same relationship, but I think you're looking at it wrong by only looking at the perpendicular part of the magnetic field.