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Re: electric charge



The comments of this thread prompted me to sketch an
introduction to electricity. Is it acceptable? I plan to
distribute it as a handout to students, after performing
standard demonstrations with rods and pith balls.
Ludwik Kowalski

Mass m is the mechanical attribute of an object. It
determines how the object accelerates (F=m*a) and
how it is attracted by another mass (F=G*m*M/d^2).
The first electric phenomenon discovered was mutual
attraction and mutual repulsion of light objects under
the influence of something which was not mass or
magnet. That something was named charge. A glass
rod robbed with silk, for example, acquires a property
of repelling another glass rod robbed with silk. That
property, named charge, was initially modeled as a fluid.
An object containing that fluid was said to be electrified.

Likewise, a plastic rod robbed with wool repels
another plastic rod robbed with wool. But an
electrified glass and an electrified plastic attract,
rather than repel, each other. This, and many other,
observation, and lead to a realization that there are
two kinds of electric fluids, positive and negative. The
term charge used to be interpreted as the "amount of
electric fluids" or "amount of electricity" which an
object can acquire or lose.

A modern interpretation is based on the realization
that submicroscopic particles, protons and electrons,
are permanently charged with positive and negative
electricity. A macroscopic object is charged when the
number of electrons and the number of protons are not
identical. An excess of protons results in a net positive
charge while an excess of electrons results in a net
negative charge. The net charge, like the total mass,
becomes an attribute of an object. It is an attribute
responsible for forces between electrified objects.
Two similar charges (both positive or both negative)
always repel but two dissimilar charges (positive and
negative) always attract. This was the first qualitative
observation about electric forces.

It turns out that the magnitude of an electric force
between two charges (q1 and q2) is proportional to
the product q1*q2 and inversely proportional to the
square of the distance (d^2) between their centers. This
observation, made by Coulomb, is known of Coulomb’s
law. It can be written as:

F = k*q1*q2 / d^2

where k is the proportionality constant. The value of
that constant can be chosen arbitrarily in order to
define a unit of electric charge. For the purpose of this
introduction the unit of electric charge, one coulomb, C,
we will defined by declaring that k=1,000,000,000. This
is equivalent to saying that the electric charge is one
coulomb if it attracts or repels an identical charge with
a force of one billion newtons when the distance between
the centers of two charges is one meter. One coulomb is
a very large charge; charges produced on robbed rods
and plates are usually expressed in microcoulombs or in
nanocoulombs. Ignoring sign differences we can say
that the charge of one electron and the charge of one
proton are identical (1.6*10^-19 C).

The so-called "official" SI definition of the unit of charge
is conceptually different from the one presented above.
But in practical terms it is not at all different. In SI the
ampere, A, is the first unit; all other electrical units are
defined in terms of kg, m, s and A. The unit of charge,
coulomb, C, is defined as A*s. In our sequence C is the
first electric unit and A will be defined as C/s. Other
nuances associated with electrical and magnetic SI units
will be discussed later. Note that F in Coulomb’s law is
positive when two charges repel (q1 and q2 have the
same sign) and negative when they attract (signs of q1
and q2 are different).


"John S. Denker" wrote:

On Friday, December 21, 2001 6:25 AM, Joe Heafner" wrote:

Another hopefully simple question. Is electric charge a
fundamental dimension or is it not? I've seen some texts
treat it as a dimension and some that do not. Which is it?

Paolo Cavallo wrote:

In the International System (SI), electric current is a
fundamental dimension. Charge is current times time.

True enough.

But then you have to decide whether there's anything
"fundamental" about SI. IMHO there isn't. SI was
chosen, and it could have been chosen differently.
http://physics.nist.gov/cuu/Units/history.html

In fact, the people who brought you the meter and
kilogram originally wanted a different definition
of the unit of time:
http://www.physics.rutgers.edu/~ransome/203/Physics203-L1.htm

=========================

In atomic physics, the charge on the electron is
taken as the unit of charge. Can you imagine how
inconvenient it would be to specify the charge on
a calcium ion in terms of the SI unit, the amp-
second? Normaly we say Ca is +2. One could
argue that this is more "fundamental", but since
I'm not a fundamentalist I'd rather just say it
was more convenient and leave it at that.

For macroscopic electrical technology and
metrology, the ampere is more convenient and
more conventional. To call it "fundamental"
would be a bit of a stretch.

By the same token, there is no law of physics
that recognizes the meter or the second as being
fundamental. They are in fact defined as arbitrary
(blatantly non-fundamental) fudge factors times a
certain natural atomic length-scale and time-scale.