# Archimedes to Hawking: Laws of Science and the Great Minds behind Them

By Clifford A. Pickover | Go to book overview

COULOMB’S LAW OF ELECTROSTATICS

France, 1785. The force of attraction or repulsion between two electric charges is proportional to the magnitude of the charges and inversely proportional to the square of their separation distance.

CROSS REFERENCE: NEWTON’S LAW OF UNIVERSAL GRAVITATION, EINSTEIN’S SPECIAL THEORY OF RELATIVITY, AND COULOMB’S LAW OF FRICTION.

In 1785, Louis XVI of France signed a law stating that a hand-
kerchief must be square. Frenchman Jean-Pierre Blanchard and
American John Jeffries were the first to cross the English Chan-
nel in a gas balloon. The dollar became the standard currency for
the United States.

Coulomb’s Law states that the magnitude of the force F between two point charges in free space is given by

where q1 and q2 are the magnitudes of the charges in coulombs, r is the distance between the charges in meters, ε0 is the permittivity of free space (8.85 × 10–9 farads/meter), and F is given in units of newtons. A coulomb, denoted by the symbol C, is defined as the amount of charge that flows past a point in a wire in one second when the current in the wire is one ampere. In other words, 1C = 1A·s. If the charges have the same sign, the force is repulsive. If the charges have opposite signs, the force is attractive.

By examining the equation, we can see that the magnitude of the force is directly proportional to the magnitude of the charges of each object and inversely proportional to the square of the distance between them. The force exerted by one point charge on the other is along the imaginary line between the charges.

Charge values may be considered to be additive in instances when electrons and protons combine to form composite particles or collections of particles. Except for the case of quarks, which are considered to have fractional charges, all charges observed in nature are integer multiples of the charge on the electron (Qe) or proton (Qp), which have these amounts of charge:

Qe = –(1.60217733 ± 0.00000049) ×10–19 coulombs
Qp = +(1.60217733 ± 0.00000049) × 10–19 coulombs

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