Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: a question from a student





On Sun, 6 Apr 1997, LUDWIK KOWALSKI wrote:

OOP, an older file was mailed a minute ago by mistake. It could be worse !

Last Thursday a student asked me why Q1 and Q2 are equal on a capacitor
connected to a battery. Would this also be true if the area of one plate
were twice as large as the other? How should I answer? Keep in mind this
is a non-calculus course and Gauss's law is not even mentioned in our text,
except in the appendix (at the end of the book).
Ludwik Kowalski


'.'<:-) (Shavings off the top of my pointy head.)

In the usual assumption that the spacing of the capacitor plates is very
small compared to their size, the excess size of one plate will go
'unused' and be uncharged. The capacitance and charge will the just about
the same as that of a capcitor made up of two plates the size of the
smaller one. The field between your mismatched plates will still be
essentially uniform between the plates, and perpendicular to the plates,
with only small fringing field which is taken as negligible. The charge
put on the larger plate will reside only on that portion of the larger
plate which is near the smaller plate.

Now, if the spacing is *not* that small, you have a more interesting
problem. However, in the design of capacitors, one usually wants to make a
device with the smallest size and material used for the desired
capacitance. Therefore you make the spacing as small as possible within
the constraint imposed by leakage (and possible breakdown) of the
dielectric at the potentials for which the capacitor is to be used. This
practical (engineering) consideration ensures that the 'small spacing'
criterion is automatically met.

Now with all the emphasis placed on "real-world" physics, why don't more
textbooks mention this very practical reason for the 'small-spacing'
treatment of capacitors? Often students think it is just a cop-out to
simplify the discussion. It also leads to an interesting discussion of how
to engineer better (i.e. smaller) capacitors, by increasing the
area/spacing ratio of the charged surfaces by clever materials science.
(See recent TPT discussion of modern capacitors.)

It it weren't for the limitations of textbooks, students might actually
learn more physics, and teachers might be freer to explore "real" physics.

-- Donald

......................................................................
Dr. Donald E. Simanek Office: 717-893-2079
Prof. of Physics Internet: dsimanek@eagle.lhup.edu
Lock Haven University, Lock Haven, PA. 17745 CIS: 73147,2166
Home page: http://www.lhup.edu/~dsimanek FAX: 717-893-2047
......................................................................