Coulomb's law

Two stationary point charges exert on each other a force directed along the line joining them. Its magnitude grows with the product of the charges and falls off rapidly with distance: doubling the separation reduces the force to a quarter. This is the law that Charles-Augustin de Coulomb measured experimentally in 1785 with his torsion balance.

Key formula — Coulomb's law

$\ev{F = k\,\frac{\abs{q_1}\,\abs{q_2}}{r^2}}$ where $k = 8{.}99\cdot 10^9\;\text{N}\,\text{m}^2/\text{C}^2 = \dfrac{1}{4\pi\varepsilon_0}$.

The constant $k$ is enormous compared with the gravitational constant $G$: this, combined with the smallness of the coulomb, tells us how intense the electric interaction is. The direction of the force depends on the signs of the charges:

• the force is repulsive if the charges have the same sign;
• the force is attractive if they have opposite signs.

In both cases the two forces — the one $q_1$ exerts on $q_2$ and the one $q_2$ exerts on $q_1$ — are equal in magnitude and opposite in direction, in agreement with Newton’s third law.

Coulomb force: like charges repel, opposite charges attract. The forces $\vec{F}_{12}$ and $\vec{F}_{21}$ are always equal and opposite (Newton’s third law).

The $1/r^2$ structure and the proportionality to the product of the “sources” make this law the electric twin of universal gravitation — a resemblance that, however, hides deep differences, discussed in the chapter’s closing reflection.

Links

Topics: Electrostatics Concepts: Coulomb’s law · Electric charge

Related exercises: Field of a point charge at 9 cm · Worked exercise — Three charges at the vertices of a triangle · Problem — Force between two 1-microcoulomb charges