The Earth itself acts like a huge bar magnet. The presence of a magnetic field about the
Earth allows us to use compasses that point northward, and creates a spectacular aurora
over the northern and southern skies. But the magnetism of the Earth is quite
complicated, and is still an active subject of research for geologists, so let us turn to the
simpler cases of idealized charges and constant magnetic fields.
Magnetic Force on Charges
The questions on magnetism that you’ll find on SAT II Physics will deal for the most part
with the reciprocal relationship between magnetic fields and moving charges. Generally,
these questions will expect you to predict the motion of a charge through a magnetic field,
or to calculate the magnitude of the magnetic force or magnetic field strength necessary
to move a charge in a certain manner.
Calculating Magnetic Force
A magnetic field exerts a force on a moving charge. Given a magnetic field, B, and a
charge, q, moving with velocity, v, the force, F, on the charge is:
Magnetic field strength is measured in teslas (T), where 1 T = 1 N/A · m.
You’ll notice that the force on a moving particle is calculated as a cross product of the
particle’s velocity and the magnetic field’s strength. You can determine the direction of
the vector by using the right-hand rule as follows: point the fingers of your right
hand in the direction of the velocity vector and then curl them around to point in the
direction of the magnetic field vector. The direction in which your thumb points gives you
the direction of the vector.
However, though q is a scalar quantity, it can affect the direction of the force vector. If q
has a negative value, then has a negative value, and so the force vector will point
in a direction opposite from what the right-hand rule might tell you.
You can calculate the magnitude of the magnetic force without using the right-hand rule,
so long as you know the angle, , between the velocity vector and the magnetic field
vector:
The sin term is important, because it lets us see very quickly that there is no force if a
charge moves parallel to a magnetic field, and that the greatest force occurs when a
charge moves perpendicular to the magnetic field.
EXAMPLE