The force exerted on a charge moving in a magnetic field is always perpendicular to both the velocity and the field. Any force perpendicular to the velocity can not change the speed (or the kinetic energy). All it can do is make the charge change direction.

If v is perpendicular to B the charge follows a circular path.

F

=

qvB

=

mv2 r

The radius of the circular path is:

r

=

mv qB

The time it takes the charge to go once around the circle is the period:

T

=

2pr v

=

2pm qB

The period is actually independent of v. This is interesting - if you take a charge and throw it into a magnetic field at various speeds, as long as the initial velocity is perpendicular to the magnetic field the radius of the circular path increases as the speed increases but the charge always takes the same time to go once around the circle.