Coulomb's law

Coulomb’s law describes the relationship between electrical charge and distance. The interaction between two electrically charged objects does not rely on actual contact between the objects, as electromagnetic force can operate over measurable distances or degrees of separation. The relationship between electrical charge and distance is fundamental in physics; indeed, it is at the center of Coulomb’s law, first formulated by French physicist Charles-Augustin de Coulomb (1736–1806) in 1785.

Background

Coulomb’s research was grounded in ancient investigations of static electricity. Ancient civilizations had observed that rubbing certain materials together appeared to give one or both of them some sort of charge. They knew that certain objects that normally possessed no attractive energy—most often rods of amber—would attract nearby objects, such as bits of paper or feathers, after being rubbed against particular substances, most often human hair or clumps of animal fur. Coulomb sought to explain and analyze this phenomenon.

Coulomb’s law is a foundational insight that has been upheld for more than two centuries of application and testing. In its algebraic formulation, it provides a conceptual introduction to the relationship between mathematics and physics. Given the quantity and type of charge of two objects and the distance between them, one can easily calculate the electrical force the objects are exerting on one another. Similarly, given the values of the charges and the electrical force, the distance between the charged objects can be derived.

Overview

Coulomb’s law deals directly with electrical forces. The strength of an electrical force is expressed as a vector, with both magnitude and direction. The direction of the electrical force depends on whether the two charged objects, or charge points, are of like or opposite charges. Like charges—that is, two positive charges or two negative charges—will repel one another; opposite charges, one positive and one negative, will attract. The magnitude, or strength, of the force is subject to a number of factors: the quantity of the electrical charge on the objects (the greater the charge, the greater the force), the method of introducing the two charged elements (drag a foot lazily across the carpet and the static charge will be relatively light; rub the foot vigorously and with great pressure, and the static charge will be jolting), and the actual distance between the two charged elements.

Coulomb reasoned that the electrical force would always be strongest when the two charged objects were closest together and that the strength of the charge would diminish as the distance between them increased, making strength and distance inversely related. Thus, Coulomb’s law states that the magnitude of the electrostatic force between two point charges is (1) directly proportional to the product of the magnitudes of the charges and (2) inversely proportional to the square of the distance separating the two objects. It is expressed mathematically by the equation below, where F is the electrical force, q₁ and q₂ are the charges of the two objects, r is the distance between them, and k_e is Coulomb’s constant, with a value of approximately 8.98755 × 10⁹ N·m²/C². If the value of F is negative, the electrical force is attractive; if it is positive, the force is repulsive. Internationally accepted values for related physical constants are regularly maintained through CODATA and the National Institute of Standards and Technology (NIST).

In its logic, Coulomb’s law is a variation on Isaac Newton’s (1642–1727) groundbreaking law of universal gravitation, which states that the force of gravity between two objects becomes stronger when they are closer together. For instance, an apple dangling from a low-hanging tree branch will fall to the ground with more force than the same apple dropped from a second-floor window. Magnitude and direction are critical factors in both Coulomb’s and Newton’s laws.

Although Coulomb’s law is a cornerstone in the field of electromagnetism, it has also been applied to the theoretical construction of the atom and of atomic motion, specifically the relationship between positively and negatively charged ions. Two oppositely charged ions attract, and two similarly charged ions repel—a phenomenon that even at the atomic level is governed by distance. The energy between two oppositely charged ions grows as the force pulling them together increases. However, at very close distances, the strong positive charge of each ion’s nucleus causes the ions to repel rather than attract one another. Coulomb’s law and its applications provide a flexible framework for approaching the relationships between electric force, matter, and motion. Coulomb’s law is important in fields such as nanotechnology, semiconductor design, plasma physics, and molecular modeling.

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