Chapter 22: Coulomb's Law

Coulomb's law, formulated in 1785, establishes that the electrical force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance separating them, following a mathematical relationship that includes the permittivity of free space as a constant. This inverse square relationship means that doubling the separation reduces the force to one quarter of its original magnitude. The nature of the force depends on charge polarity: like charges experience repulsive forces while opposite charges experience attractive forces. Electric field strength, defined as the force per unit positive charge at any location, is a vector quantity that also obeys the inverse square law and decreases with distance from a source charge. Electric potential represents the energy per unit charge at a point in an electric field, with the reference point conventionally set at infinity where potential equals zero. Unlike field strength, potential is a scalar quantity, allowing potentials from multiple sources to be combined through simple algebraic addition. The relationship between field strength and potential is expressed through the potential gradient, where the field strength equals the negative rate of change of potential with distance, indicating that electric fields point from regions of higher to lower potential. The chapter emphasizes the mathematical and conceptual parallels between electric and gravitational fields, both exhibiting radial patterns around point sources and uniform patterns between parallel configurations, both following inverse square laws, and both having scalar potentials. However, fundamental differences exist: gravitational interactions arise exclusively from mass and are purely attractive, while electrical interactions originate from charges and permit both attractive and repulsive forces depending on charge signs. Understanding these concepts provides the foundation for analyzing electrostatic phenomena and forms the basis for more complex electric field analysis.