Moving reference frames

A peculiar aspect of the magnetic force is that it depends on the particle's velocity. All other forces encountered depend only on the relative distance. This dependence is strange because the velocity depends on the reference frame of the observer. Imagine a charge q resting on your desk. If you are in a magnetic field the charge feels no force because the velocity of the charge is zero. Now imagine your desk is on a planet which is speeding through space filled with magnetic field (as it in fact is). What does one use for the velocity of the charge? It appears totally arbitrary, but the force the charge feels is not arbitrary. For instance, either the charge is being pulled off the planet by the magnetic force or it is not.

The solution to this paradox lies in extremely intricate notions of the theory of special relativity. Later in the semester, we will study some aspects of relativity such as the fact that moving objects appear slower and that moving clocks run slower. One consequence of relativity is that if one observer measures a magnetic field but no electric field, another observer who is moving relative to the first will see both magnetic and electric fields. The physical effect of the combined magnetic and electric forces will be the same for both observers.