A charge of 5 C moves upward at 2 m/s in a magnetic field of 0.3 T that points into the
page. What is the magnitude and direction of the force that the charge experiences?The cross product of is a vector of magnitude qvB sin = 3 N. Following the right-
hand rule, point your fingers toward the top of the page, and then curl them around so
that they point into the page. You’ll find that your thumb is pointing left, which is the
direction of the vector. Because the value of q is positive, the force acting on the
particle will also be in the leftward direction.
A Quick Note on Vectors Going In and Out of the Page
The magnetic field lines illustrated in this example that are going into the page are
represented by circles with an “x” inscribed in them. Vector lines pointing out of the page
are represented by circles with a dot in them. You can think about these symbols as
arrows appearing from in front or behind: from in front, you see the conical tip of the
arrow, and from behind you see the fletching of the four feathers in an “x” shape.
Trajectory of Charges in a Magnetic Field
The direction of the force on a moving charge depends on the direction of its velocity. As
its velocity changes, so will its direction. The magnitude of the velocity will not change,
but charged particles moving in a magnetic field experience nonlinear trajectories.
When the Velocity Vector and Magnetic Field Lines Are
Perpendicular
In the example above, we saw that a force of 3 N would pull the charged particle to the
left. However, as soon as the particle begins to move, the velocity vector changes, and so
must the force acting on the particle. As long as the particle’s velocity vector is at a right
angle to the magnetic field lines, the force vector will be at right angles to both the
velocity vector and the magnetic field. As we saw in the chapter on circular motion and
gravitation, a force that always acts perpendicular to the velocity of an object causes that
object to move in circular motion.