PASCO ES-9070 COULOMB BALANCE - Manual (Page 6)

Coulomb Balance 012-03760E
2
Theory
Take one gram of protons and place them one meter away
from one gram of electrons. The resulting force is equal to
1.5 x 10 23 newtons—roughly the force it would take to
“lift” an object from the surface of the Earth that had a
mass about 1/5 that of the moon—not a small force.
So, if such small amounts of charge produce such
enormous forces, why does it take a very delicate torsion
balance to measure the force between charged objects in
the laboratory? In a way, the very magnitude of the forces
is half the problem. The other half is that the carriers of the
electrical force—the tiny proton and the even tinier
electron—are so small, and the electrons are so mobile.
Once you separate them, how do you keep them
separated? The negatively charged electrons are not only
drawn toward the positively charged protons; they also
repel each other. Moreover, if there are any free electrons
or ions between the separated charges, these free charges
will move very quickly to reduce the field caused by the
charge separation.
So, since electrons and protons stick together with such
tenacity, only relatively small charge differentials can be
sustained in the laboratory. This is so much the case that,
even though the electrostatic force is more than a billion-
billion-billion-billion times as strong as the gravitational
force, it takes a very delicate torsion balance to measure
the electrical force, whereas we can measure the
gravitational force by weighing an object with a spring
balance.
ä NOTE: The torsion balance gives a direct and
reasonably accurate measurement of the Coulomb
force. The most accurate determinations of
Coulomb's law, however, are indirect. It can be
shown mathematically that if the inverse square law
holds for the electrostatic force, the electric field
inside a uniformly charged sphere must be
everywhere zero. Measurements of the field inside a
charged sphere have shown this to be true with
remarkable accuracy. The Coulomb force can be
expressed by the formula:
F = kq
1
q
2
/R 2+n .
Using this indirect method, it has been demonstrated
experimentally that n ­ 2 x 10 –16 .