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# fundamental practical EM quantities

• From: John Denker <jsd@AV8N.COM>
• Date: Sat, 14 Feb 2004 10:32:51 -0800

Here are some interesting exercises:
1) Consider epsilon_naught, the fundamental constant used in
practical capacitance problems. Express it in *practical*
2) Consider mu_naught, the fundamental constant used in
practical inductance problems. Express it in *practical*
units, i.e. microhenries per meter.

I remember these quantities in this form, and only in this form.

a) Note the scaling property: each is extensive, "per meter".
In more detail: each scales like the ratio of some area to
some length.
b) Get a feel for the size: what is the inductance of a trash
can (i.e. one-turn inductor) that is 1m tall and 1m in diameter?
c) Similarly, what is the inductance of a wedding ring?
d) Similarly, what is the capacitance of a pair of dice made of
some conductive material, each 1cm on a side and placed 1mm
apart?
e) Don't be too surprised if you sometimes see 1.257 expressed
as 4pi/10.
f) It's always fun to calculate 1/sqrt(epsilon_naught * mu_naught).

I long ago committed these results to memory. I find them quite
useful, more useful than the more formal, abstract view of such
things found in most textbooks.

Obviously this only makes sense if/when the students previously
(or perhaps concurrently) have some experience handling practical
capacitors denominated in pF and practical inductors denominated
in muH. But you want to get to this point one way or another,
where EM theory makes contact with practical experience.