Introduction to SAT II Physics - FreeExamPapers

Because the velocity vector and the magnetic field lines are at right angles to one another,
the magnitude of the magnetic force is F = qvB. Furthermore, because the magnetic force
pulls the particle in a circular path, it is a centripetal force that fits the equation F =
mv 2 /r. Combining these two equations, we can solve for r to determine the radius of the
circle of the charged particle’s orbit:
When the Velocity Vector and Magnetic Field Lines Are Parallel
The magnetic force acting on a moving charged particle is the cross product of the
velocity vector and the magnetic field vector, so when these two vectors are parallel, the
magnetic force acting on them is zero.
When the Velocity Vector and Magnetic Field Lines Are Neither
Perpendicular nor Parallel
The easiest way to deal with a velocity vector that is neither parallel nor perpendicular to
a magnetic field is to break it into components that are perpendicular and parallel to the
magnetic field.
The x-component of the velocity vector illustrated above will move with circular motion.
Applying the right-hand rule, we find that the force will be directed downward into the
page if the particle has a positive charge. The y-component of the velocity vector will
experience no magnetic force at all, because it is moving parallel to the magnetic field
lines. As a result, the charged particle will move in a helix pattern, spiraling around while
also moving up toward the top of the page. Its trajectory will look something like this:
If the particle has a positive charge it will move in a counterclockwise direction, and if it
has a negative charge it will move in a clockwise direction.
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