# A report onMaxwell's equations and Faraday's law of induction

The Maxwell–Faraday equation (listed as one of Maxwell's equations) describes the fact that a spatially varying (and also possibly time-varying, depending on how a magnetic field varies in time) electric field always accompanies a time-varying magnetic field, while Faraday's law states that there is emf (electromotive force, defined as electromagnetic work done on a unit charge when it has traveled one round of a conductive loop) on the conductive loop when the magnetic flux through the surface enclosed by the loop varies in time.

The Maxwell–Faraday version of Faraday's law of induction describes how a time-varying magnetic field corresponds to curl of an electric field.

- Maxwell's equations

## Magnetic field

Vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials.

Vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials.

In a modified form that accounts for time varying electric fields, Ampère's law is one of four Maxwell's equations that describe electricity and magnetism.

are called the Ampère–Maxwell equation and Faraday's law respectively.

## Lorentz force

Combination of electric and magnetic force on a point charge due to electromagnetic fields.

Combination of electric and magnetic force on a point charge due to electromagnetic fields.

Variations on this basic formula describe the magnetic force on a current-carrying wire (sometimes called Laplace force), the electromotive force in a wire loop moving through a magnetic field (an aspect of Faraday's law of induction), and the force on a moving charged particle.

The electric field in question is created by the changing magnetic field, resulting in an induced EMF, as described by the Maxwell–Faraday equation (one of the four modern Maxwell's equations).

## Electromagnetic induction

Production of an electromotive force across an electrical conductor in a changing magnetic field.

Production of an electromotive force across an electrical conductor in a changing magnetic field.

Michael Faraday is generally credited with the discovery of induction in 1831, and James Clerk Maxwell mathematically described it as Faraday's law of induction.

Faraday's law was later generalized to become the Maxwell–Faraday equation, one of the four Maxwell equations in his theory of electromagnetism.