Having established this equation, let us take a moment to analyze
its implications. First, it is clear that a charge moving parallel to the
magnetic field experiences no force, as the cross product is zero. Second, the
magnitude of the force on the charge varies directly not only with the magnitude
of the charge, but of the velocity as well. The faster a charged particle
travels, the more force it will feel in the presence of a given magnetic field.
This equation forms a basis for our study of electromagnetism.
From it we will be able to derive the fields created by various wires and
magnets, and derive some properties of the magnetic field.
Relating Magnetic and Electric Forces
Using the definition of the magnetic field we have just developed, we become
able to generate a complete expression for the force exerted on a charged
particle, q, in the presence of both electric and magnetic fields. Recall that
in the presence of an electric field alone the force felt by a point charge q is
simply proportional to the field at that point, or F = qE. Thus, if this point
charge is in the presence of both an electric field and a magnetic field, we can
find the total force on the charge by simple vector addition:
This equation only applies to vector quantities--usually the force due to the
electric field and the magnetic field are not in the same direction, and cannot
be added algebraically.
= q
+ 
