* Of the four Maxwell's equations, two — Faraday's law and Ampère's law — can be compactly expressed using curl.

In fact, formulas for physical laws of electromagnetism ( such as Maxwell's equations ) need to be adjusted depending on what system of units one uses.

According to Chalmers, a naturalistic account of property dualism requires a new fundamental category of properties described by new laws of supervenience ; the challenge being analogous to that of understanding electricity based on the mechanistic and Newtonian models of materialism prior to Maxwell's equations.

According to Maxwell's equations, a spatially varying electric field causes the magnetic field to change over time.

The speed of light and other EMR predicted by Maxwell's equations did not appear unless the equations were modified in a way first suggested by FitzGerald and Lorentz ( see history of special relativity ), or else otherwise it would depend on the speed of observer relative to the " medium " ( called luminiferous aether ) which supposedly " carried " the electromagnetic wave ( in a manner analogous to the way air carries sound waves ).

Electromagnetic waves as a general phenomenon were predicted by the classical laws of electricity and magnetism, known as Maxwell's equations.

Inspection of Maxwell's equations without sources ( charges or currents ) results in, along with the possibility of nothing happening, nontrivial solutions of changing electric and magnetic fields.

Beginning with Maxwell's equations in free space:

In classical electromagnetism, the electromagnetic field obeys a set of equations known as Maxwell's equations, and the electromagnetic force is given by the Lorentz force law.

According to Maxwell's equations, the speed of light in a vacuum is a universal constant, dependent only on the electrical permittivity and magnetic permeability of free space.

The way in which charges and currents interact with the electromagnetic field is described by Maxwell's equations and the Lorentz force law.

These interactions are described by Maxwell's equations and the Lorentz force law.

Maxwell's equations relate ( a ) the presence and movement of charged particles with ( b ) the generation of fields.

However, if either the electric or magnetic field has a time-dependence, then both fields must be considered together as a coupled electromagnetic field using Maxwell's equations.

Maxwell's equations can be written in tensor form, generally viewed by physicists as a more elegant means of expressing physical laws.

The behaviour of electric and magnetic fields, whether in cases of electrostatics, magnetostatics, or electrodynamics ( electromagnetic fields ), is governed in a vacuum by Maxwell's equations.

Inside a linear material, Maxwell's equations change by switching the permeability and permittivity of free space with the permeability and permittivity of the linear material in question.

These equations are derived from Maxwell's equations.

James Clerk Maxwell was the first to obtain this relationship by his completion of Maxwell's equations with the addition of a displacement current term to Ampere's Circuital law.

The resulting equations can be separated into further sets of equations, one of which is equivalent to Einstein field equations, another set equivalent to Maxwell's equations for the electromagnetic field and the final part an extra scalar field now termed the " radion ".

Maxwell's idea was to take three separate black-and-white photographs through red, green and blue filters.

By eliminating ρ and J, using Maxwell's equations, and manipulating using the theorems of vector calculus, this form of the equation can be used to derive the Maxwell stress tensor σ, in turn this can be combined with the Poynting vector S to obtain the electromagnetic stress-energy tensor T used in general relativity.

Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits.

Maxwell's equations are named after the Scottish physicist and mathematician James Clerk Maxwell, since in an early form they are all found in a four-part paper, " On Physical Lines of Force ", which he published between 1861 and 1862.

The form used in Maxwell's equations is always valid but more restrictive than that originally formulated by Michael Faraday.

In 1884 he recast Maxwell's mathematical analysis from its original cumbersome form ( they had already been recast as quaternions ) to its modern vector terminology, thereby reducing twelve of the original twenty equations in twenty unknowns down to the four differential equations in two unknowns we now know as Maxwell's equations.

Heaviside employed the curl and divergence operators of the vector calculus to reformulate 12 of these 20 equations into four equations in four variables ( B, E, J, and ρ ), the form by which they have been known ever since ( see Maxwell's equations ).

One good example is classical electromagnetism, which encompasses results derived from gauge symmetry ( sometimes called gauge invariance ) in a form of a few equations called Maxwell's equations.

It is one of the four Maxwell's equations which form the basis of classical electrodynamics, the other three being Gauss's law for magnetism, Faraday's law of induction, and Ampère's law with Maxwell's correction.

Starting with Gauss ' law for electricity ( also one of Maxwell's equations ) in differential form, we have:

A good example is classical electromagnetism, which encompasses results derived from gauge symmetry ( sometimes called gauge invariance ) in a form of a few equations called Maxwell's equations.

It appears frequently in physics in places like the differential form of Maxwell's Equations.

Maxwell's equations can also be expressed in a generally covariant form, which is as invariant under general coordinate transformation as Einstein's field equation.

He argued that Maxwell's heat problem might be avoided by assuming that the absorbed energy is not be converted into heat, but re-radiated in a still more penetrating form.

Mathematics would not qualify as a language under these definitions, as it is primarily a written form of communication ( to see why, try reading Maxwell's equations out loud ).

Hoagland has proposed a form of physics he calls " hyperdimensional physics " which, supported by the work of pseudoscientific overunity claimant Thomas E. Bearden, he claims to represent the full implementation of James Clerk Maxwell's original 20 quaternion equations, instead of the reduced Maxwell's equations as amended by Oliver Heaviside commonly taught today.

To obtain the electromagnetic wave equation in a vacuum using the modern method, we begin with the modern ' Heaviside ' form of Maxwell's equations.

In Maxwell's papers, the time varying aspect of electromagnetic induction is expressed as a differential equation which Oliver Heaviside referred to as Faraday's law even though it is slightly different in form from the original version of Faraday's law, and does not describe motional EMF.

Heaviside's version ( see Maxwell – Faraday equation below ) is the form recognized today in the group of equations known as Maxwell's equations.

This relation is known as Gauss ' law for electric field in its integral form and it is one of the four Maxwell's equations.

Skrotskii realized that electromagnetic field equations in a curved spacetime can be written in a non-covariant form formally equivalent to Maxwell's equations in a macroscopic medium in flat spacetime.