Magnetic field is expressed in SI units as a tesla (T), which is also
called a weber per square meter:
The direction of F is found from the right
‐hand rule, shown in Figure 1. Using the right-hand rule you
can find the direction of magnetic force on a moving charge.
To find the direction of the force on the charge, with a flat hand point
your thumb in the direction of the velocity of the positive charge and your
fingers in the direction of the magnetic field. The
direction of the force is
out of the palm of your hand. (If the moving charge is negative, point your
thumb opposite to its direction of motion.) Mathematically, this force is the
cross product of the velocity vector and the magnetic field vector.
If the velocity of the charged particle is perpendicular to the uniform
magnetic field, the force will always be directed
toward the center of a
circle of radius r, as shown in Figure 2. The x symbolizes a magnetic field
into the plane of the paper - the tail of the arrow. (A dot symbolizes a vector
out of the plane of the paper - the tip of the arrow.)
The magnetic force provides centripetal
acceleration:
, or
The radius of the path is proportional
to the mass
of the charge. This equation underlies the operation of a mass spectrometer,
which can separate equally ionized atoms of slightly different masses. The
singly ionized atoms are given equal velocities, and because their charges
are the same and they travel through the same B, they will travel in slightly
different paths and can
then be separated.
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