Which equations include Faraday's law as one of their four classical laws?

Faraday’s law is one of the four classical laws expressed by Maxwell’s equations.

Maxwell’s equations form the mathematical foundation of classical electromagnetism. In their standard modern form, the four equations are Gauss’s law, Gauss’s law for magnetism, Faraday’s law of induction, and the Ampère–Maxwell law. Together they describe how electric and magnetic fields are produced and how they influence one another.

Faraday’s law states that a changing magnetic flux produces an electric field. In differential form, it is commonly written as curl E = −∂B/∂t. The negative sign expresses Lenz’s law: the induced effect opposes the change that produces it. This principle explains the operation of generators, transformers, and many electrical technologies.

The equations carry both Faraday’s experimental legacy and Maxwell’s theoretical synthesis. Maxwell used Faraday’s concept of lines of force in developing electromagnetic theory, while later work by Oliver Heaviside and others produced the compact four-equation vector form familiar today. A common mix-up is to call Faraday’s law itself “Maxwell’s equation”; more precisely, it is one member of the set called Maxwell’s equations.