Magnetism the Most Magical of Forces

Nothing impresses a child more than magnets.  OK, maybe balloons, but magnets are a close second.  Give two magnets to a five year old and that is a solid hour of entertainment right there.  The magnetic force is not like the 'ever-present' gravity in our day-to-day lives.  It seems to be the result of some special, 'magical' force that we observe from time to time.

At the start of my electricity and magnetism course, I usually emphasize that although the electrostatic and magnetic forces are of the same family of forces, they must not be confused as the same thing.  The average person interacts with both of these forces daily and has little understanding of either.  It takes a while to wrap one's head around magnetism, but let's give it a try...

The mere presence of a charge creates an electric field, which can exert an electrostatic force upon another charge.  This is the basis of electrostatics.  In order for a magnetic field to be produced, charge must be in motion.  It then follows that for a charge to experience a magnetic force within a magnetic field, it too must be in motion.  This is the basis of magnetism.  So, whereas all charges produce and respond to electric fields, only those in motion produce and respond to magnetic ones.

The electrostatic force acting on a charged particle in an electric field is quite straight forward:

Here, charge q responds to electric field E.  What makes this force kind of intuitive is that the force points along the same axis or exactly opposite to that of the field (depending on the sign of the charge).  Contrast that with the magnetic force, which acts on a charged particle as follows: