#### BELIEVE ME NOT! **-** **-** A SKEPTIC's GUIDE

** Next:** The Point Source

If you go on in Physics you will learn all about GAUSS' LAW
along with vector calculus in your advanced course on
ELECTRICITY AND MAGNETISM,
where it is used to calculate the electric field
strength at various distances from highly symmetric distributions
of electric charge. However, GAUSS' LAW can be applied
to a huge variety of interesting situations
having nothing to do with electricity except by analogy.
Moreover, the rigourous statement of GAUSS' LAW
in the mathematical language of vector calculus
is not the only way to express this handy concept, which is
one of the few powerful modern mathematical tools which can be
accurately deduced from "common sense"
and which really follows from a statement so simple and
obvious as to seem trivial and uninteresting, to wit:

(Colloquial form of GAUSS' LAW)

*"When something passes **out* of a region,

it is no longer *inside* that region."

How, you may ask, can such a dumb tautology teach us
anything we don't already know?
The power of GAUSS' LAW rests in its combination with
our knowledge of *geometry* (*e.g.* the surface area *A*
of a sphere of radius *r* is
)
and our instinctive
understanding of *symmetry* (*e.g.* there is no way for
a *point* of zero size to define a favoured *direction *).
When we put these two skills together with GAUSS' LAW
we are able to easily derive some not-so-obvious
*quantitative* properties of many commonly-occurring
natural phenomena.

** Next:** The Point Source

Jess H. Brewer -
Last modified: Mon Nov 16 17:24:55 PST 2015