The magnetic and electric fields are force fields. They exert
forces on magnetic or charged particles. We can measure these
fields easily with instruments that respond to such forces.
Magnetic and electric fields therefore have a very real and
tangible existence. But these force fields themselves are merely
higher order expressions of something more fundamental known as
potential fields. Potential fields form an underlying substrate
in which certain distortions give rise to magnetic or electric
fields. But even without such distortions, and hence without any
measurable magnetic or electric fields, the potential field can
still exist in its distortion-free state. There are three main
potential fields: magnetic vector potential `vec(A)`, scalar
electric potential `V`, and gravitational potential `varphi`.
These respectively give rise to the three main force fields:
magnetic field `vec(B)`, electric field `vec(E)`, and
gravitational field `vec(g)`. The following equations show how
these relate: `grad xx vec(A) =