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Maxwell and The Nerds
It takes a few years of university­level physics to understand these
equations. They are written using a branch of mathematics called
vector calculus. A vector, written in bold­face type, is any
quantity with both a magnitude and a direction. Sixty miles an
hour isn't a vector, but sixty miles an hour due north on Highway
1 is. E and B represent the electric and magnetic fields. The
triangle, called a nabla (because of its resemblance to a certain
ancient Middle Eastern harp), expresses how the electric or
magnetic fields vary in three­dimensional space. The 'dot product'
and the 'cross product' after the nablas are statements of two
different kinds of spatial variation.
and
represent the time variation, the rate of change of the
electric and magnetic fields. j stands for the electrical current. The
lower­case Greek letter p (rho) represents the density of electrical
charges, while ε 0 (pronounced 'epsilon zero') and μ 0 (pronounced
'mu zero') are not variables, but properties of the substance E and
B are measured in, and determined by experiment. In a vacuum,
ε 0 and μ 0 are constants of nature.
Considering how many different quantities are being brought
together in these equations, it's striking how simple they are. They
could have gone on for pages, but they don't.
The first of the four Maxwell equations tells how an electric
field due to electrical charges (electrons, for example) varies with
distance (it gets weaker the farther away we go). But the greater
the charge density (the more electrons, say, in a given space), the
stronger the field.
The second equation tells us that there's no comparable statement
in magnetism, because Mesmer's magnetic 'charges' (or
magnetic 'monopoles') do not exist: saw a magnet in half and you
won't be holding an isolated 'north' pole and an isolated 'south'
pole; each piece now has its own 'north' and 'south' pole.
The third equation tells us how a changing magnetic field
induces an electric field.
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