At this time of the year electricity is upon us. I am posting a quotation
from the draft of an article (sent to The Science Teacher by Ellis Noll)
about the way of teaching Coulomb's law. How do you deal with the dilemma
described in the third paragraph?
Ludwik Kowalski
..........................................................................
..... The sequence on electricity begins with electrostatics. We establish
the existence of two kinds of charge and proceed with an introduction of
Coulomb's law. .... At least three major aspects of that law must eventually
be recognized by students. The first is the inverse square of distance
relation, the second is the proportionality of the force to the product of
two charges, and the third is the issue of the unit of charge. Most textbooks
simply give students the SI version of Coulomb's law and proceed with the
analysis of its mathematical consequences. Our approach is different. ....
[this is followed by the description of an experiment]. .......
It is important to emphasize that no absolute unit of charge was necessary
to show that the force between two conducting spheres is directly proportional
to the product of charges and inversely proportional to the square of the
distance between their centers. Numerical data were expressed in terms of
whatever charge was initially delivered to the interacting spheres. The next
logical step is to turn the relation of proportionality into an equality.
Unfortunately, the numerical factor 9*109, appearing in Coulomb's force law,
cannot be explained without introducing the unit of charge, coulomb.
That unit is defined as the product of ampere and second. How can we introduce
the coulomb unit without violating the rule of ideal teaching? The rule calls
for logical continuity; it does not allow us to explain something today in
terms of what is going to be explained tomorrow. In practice the rule is often
violated but this is not desirable. What should we do? Should the teaching
sequence be changed to accommodate the logic of SI units (4)? Or should we
violate the teaching rule and tell students that we are "borrowing from
tomorrow"? We are aware of this dilemma but have no clear idea how to resolve
it.
One possibility is to define Coulomb in terms of number of electrons and to
state, without an explanation, that an electron is a natural unit of charge.
This approach, found in some textbooks, is less confusing than giving students
the formula with 4*PI*epsilon. It turns out that research physicists often use
a system of units in which one electron is the unit of charge.
The mathematical similarities between Coulomb's law and the law of universal
gravitation should not prevent us from seeing a big difference between the
ways in which these two fundamental relations are introduced to students. The
law of universal gravitation is usually introduced when students are already
familiar with the concept of inertial mass and with the mass unit. The basic
law of electrostatics, on the other hand, is usually introduced in the first
unit (chapter) of electricity. The concept of charge, the unit of charge, and
the force law must be learned at the same time. This creates many conceptual
difficulties.