Coulomb's Law

"When man wanted to make a machine that would walk he created the wheel, which does not resemble a leg"
Guillaume Apollinaire

The magnitude of the force of attraction (or repulsion), F₁₂ between two point charges q₁ and q₂ is given by Coulomb's Law.

where R₁₂ is the distance between the charges. k is a constant of proportionality known as the Coulomb constant, having the value 9 x 10⁹ N.m² / C² in a vacuum.

Note that the Coulomb constant, k, is often replaced with (1/4π ε₀), where ε₀is the permittivity of the vacuum (more later).

The direction of this force is along the line joining the two charges with the sense determined by the relative signs of the charges

Note that the force on each charge has the same magnitude (as required by Newton's third law of motion).

For two 1 Coulomb charges separated by 1 metre the magnitude of the force is given by,
F = (9 x 10⁹ x 1 x 1 )/ 1 = 9 x 10⁹ Newtons
This is an extremely large force (sufficient to move Mt. Everest with an acceleration of 1cm/s²). The Coulomb is a very large unit. Typical macroscopic charges are measured in micro-coulombs (10^-6 C).
To handle situations with more than one charge, the charges must be treated in pairs, so that the overall force on one charge will be the vector sum of the force due to each of the other charges. For example the force on q₁ due to all other charges q₂, q₃ , q₄... would be given by,

F₁ = F₂₁ + F₃₁ + F₄₁ + ...

Notice the similarity of Coulomb's Law to Newton's Law of Gravitation

both are "inverse square" laws. Substitute charge for mass and "k" for "G" and you have Coulomb's law.

The relative magnitudes of the Coulomb constant, k = 9 x 10⁹ and the gravitational constant, G = 6.67 x 10^-11, is an indication of the relative strengths of the two forces. The electrical force of attraction is much, much stronger than the gravitational force of attraction.

"The wireless telegraph is not difficult to understand. The ordinary telegraph is like a very long cat. You pull the tail in New York, and it meows in Los Angeles. The wireless is the same, only without the cat."
Albert Einstein

Dr. C. L. Davis
Physics Department
University of Louisville
email: c.l.davis@louisville.edu