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Let us consider a charge q with velocity
entering a region of space with a constant magnetic field .
We assume that initially and are at right angles.
The charge will experience the force of Eq.(1.2) which,
by definition, is perpendicular to the velocity . Because
of this, the force does no work on the charge (recall
W = Fdcos = 0
if
= 90^{ o }), and because
W = K = (mv^{ 2})
the speed of the charge will not change. It turns out that the charge
will move in a circular motion, with a (centripetal) acceleration
directed
toward the center of the circle, as illustrated in
Fig. 1.3.
Figure 1.3:
Motion of a charged particle in a magnetic field

For such a motion we have the following relation:
This behaviour of a charged particle in a magnetic field is the principle
behind machines such as mass spectrometers, which can be used
to measure the masses of charged particles by measuring their radii
of curvature in a magnetic field.
Next: Magnetic Force on a
Up: Magnetism
Previous: The Magnetic Field
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10/9/1997