The Electric Force


September 30, 2019

The Electric Force

The Electric Force

The electric charge unit is the Coulomb, C. Ordinary matter consists of atoms containing charged protons (+1.6 x 10-19 C) and electrons (-1.6 x 10-19 C). Electric charge is quantized as a multiple of the electron or proton charge.

The influence of separate charges is quantified in terms of the forces between them, which are given by Coulomb's law of electric force:

The electric force

And the electric fields and voltages produced by them.

Here is the thing: one Coulomb of charge flows through a 120-watt lightbulb (120 volts AC) in one second. Two charges of one Coulomb each separated by a distance of one meter repel each other with a force of about a million tons:

The electric force

How does this work out, and why don't we notice it? 


Well, U.S. household circuits operate on 120 volts AC. From the electric power relationship:

P is the power in Watts units, W. I is the current in Ampere units. V is the voltage that uses power at the rate of 120 W on a 120 V circuit. That requires an electric current of 1 Amp.

One ampere of current carries one Coulomb of charge per second through the circuit. So, one Coulomb of charge is the charge transported through a 120 W lightbulb in one second.

If two one-second collections of one Coulomb each are separated at points one meter apart, the force between them, according to Coulomb's law, will be:

The electric force

So, the repulsive electric force is nine billion Newtons, or about 1.01 million tons. Okay, that is what the math says. But we don't see such a dramatic effect because there are never many departures from electrical neutrality at a given point in a circuit.

A Coulomb of charge at one point does not exist in nature. Copper metal is an excellent electrical conductor due to a valence electron being free to move about in the solid. The density of copper is 9 grams per cubic centimeter. One mole of copper weighs 63.5 grams, so one cubic centimeter of copper contains about 1/7th of a mole, or about 8.5 x 1022 copper atoms.

FYI: one mole (mol) of a pure substance is a mass of the material in grams that is numerically equal to the molecular mass in atomic mass units. For instance, copper, it is 63.5 g.

The gravitational force acting on a 9-gram copper sphere is:

Since the net charge resides at the points of the spheres farthest from each other because of charge repulsion, that repulsive force is equal to the weight of a sphere.

The radius of a one cubic centimeter sphere of copper is 0.62 cm. So, the distance between the point charges through which the above force acts is two sphere diameters, that is 2.48 cm.

Coulomb's law

gives a charge of:

which when compared to the total mobile charge of 13,600 C, is the same as removing one valence electron out of every

electrons from each copper sphere.

The electric force

So, removing just one in a trillion of the free electrons from each copper sphere causes enough electric repulsion on the top sphere to overcome gravity and lift it. Think about that. The slight departure from electrical neutrality is so powerful that it counters the entire planet's pull. That demonstrates how feeble gravity is compared to the force dominating the Universe: the Electric Force.