* 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.

Maxwell's equations take the form of an electromagnetic wave in an area that is very far away from any charges or currents ( free space ) – that is, where and are zero.

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 Laws, which unify light, fields, and charge are one of the great milestones of theoretical physics.

Grand Unification is reminiscent of the unification of electric and magnetic forces by Maxwell's theory of electromagnetism in the 19th century, but its physical implications and mathematical structure are qualitatively different.

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.

It is often useful to write Maxwell's equations in other forms ; these representations are still formally termed " Maxwell's equations ".

While Maxwell's equations are consistent within special and general relativity, there are some quantum mechanical situations in which Maxwell's equations are significantly inaccurate: including extremely strong fields ( see Euler – Heisenberg Lagrangian ) and extremely short distances ( see vacuum polarization ).

Maxwell's equations are usually an extremely accurate approximation to the more accurate theory of quantum electrodynamics.

Moreover, Maxwell's equations, the foundation of classical electrodynamics, are Lorentz-invariant.

In Maxwell's equations, the forces between particles are mediated by electric and magnetic fields.

It also accounted for anomalous observations, including the properties of black body radiation, that other physicists, most notably Max Planck, had sought to explain using semiclassical models, in which light is still described by Maxwell's equations, but the material objects that emit and absorb light, do so in amounts of energy that are quantized ( i. e., they change energy only by certain particular discrete amounts and cannot change energy in any arbitrary way ).

The interaction terms are similar in spirit to those in Maxwell's equations, being interactions between fields.

It has always been the case that time and space are measured using real numbers, and the suggestion that the dimensions of space and time are comparable could have been raised by the first people to have formalized physics, but ultimately, the contradictions between Maxwell's laws and Galilean relativity had to come to a head with the realization of the import of finitude of the speed of light.

The set of equations which describe MHD are a combination of the Navier-Stokes equations of fluid dynamics and Maxwell's equations of electromagnetism.

Since E and P are defined separately, this equation can be used to define D. The physical interpretation of D is not as clear as E ( effectively the field applied to the material ) or P ( induced field due to the dipoles in the material ), but still serves as a convenient mathematical simplification, since Maxwell's equations can be simplified in terms of free charges and currents.

In probability theory, Maxwell's theorem, named in honor of James Clerk Maxwell, states that if the probability distribution of a vector-valued random variable X = ( X < sub > 1 </ sub >, ..., X < sub > n </ sub > )< sup > T </ sup > is the same as the distribution of GX for every n × n orthogonal matrix G and the components are independent, then the components X < sub > 1 </ sub >, ..., X < sub > n </ sub > are normally distributed with expected value 0, all have the same variance, and all are independent.

The name of Slade's persona " Maxwell Demon " was named after Brian Eno's first band, which in itself was influenced by James Clerk Maxwell's thought experiment character, " Maxwell's demon ".

Maxwell's nicknames included " Paw Paw ," ( given by the Detroit Tigers announcer Van Patrick because of Maxwell's unusually named hometown of Paw Paw, Michigan ), " Smokey ," " Sunday Charlie ", and " the Sabbath Smasher ," the latter two given in recognition of his propensity for hitting home runs on Sundays.

Attempts to unify those models or to create a complete mechanical description of them did not succeed, but after considerable work by many scientists, including Michael Faraday and Lord Kelvin, James Clerk Maxwell ( 1864 ) developed an accurate theory of electromagnetism by deriving a set of equations in electricity, magnetism and inductance, named Maxwell's equations.

A ship salvaged at Asmara by Navy Commander Edward Ellsberg working under Maxwell's direction was named for General Maxwell.

Still, Thomson's model ( along with a similar Saturnian ring model for atomic electrons, also put forward in 1904 by Nagaoka after James Clerk Maxwell's model of Saturn's rings ), were earlier harbingers of the later and more successful solar-system-like Bohr model of the atom.

Even after experiments showed that Einstein's equations for the photoelectric effect were accurate, resistance to the idea of photons continued, since it appeared to contradict Maxwell's equations, which were well-understood and verified.

The original townsite, located on land owned by C. A. McMillen, was first called Old Decator, after McMillen's hometown, and later, Maxwell's Branch.

After Lois Maxwell's death, Roger Moore recalled that she would have liked to have seen Moneypenny become the new M after Moore's retirement.

Campbell's loyalty to Maxwell was demonstrated when he punched The Guardian journalist Michael White after White joked about " Captain Bob, Bob, Bob ... bobbing " in the Atlantic Ocean shortly after Maxwell's drowning in 1991.

If the potential is a solution to Maxwell's equations then, after this gauge transformation, the new potential is also a solution to Maxwell's equations and no experiment can distinguish between these two solutions.

# A Bigger Splash ( December 20, 1992 ) – Soon after purchasing Robert Maxwell's luxury yacht, the Lady Ghislaine, at auction for £ 10 million, Alan announces that he will use the yacht to transport a cargo of humanitarian aid to war-torn Herzegovina, a move that will coincide with the beginning of Piers ' peace conference between the region's two warring factions.

In the course of the robbery, three people are killed: a security guard that Maxwell kills for his keys ; DiGiorgio, whom Maxwell stabs in the back after he stumbles in on the robbery after discovering the guard's body ; one of Maxwell's accomplices is accidentally shot when DiGiorgio's gun goes off.

The military police raided the party and called the local police for assistance after confronting Maxwell's group.

Maxwell's medals are now held in the Lord Ashcroft collection after sale at auction.

The notion of the ether as a compressible fluid or similar physical entity was too deeply ingrained in nineteenth century physical thinking, even for decades after the publication of Maxwell's electromagnetic theory in 1864.

The problems and solutions were originally published anonymously, but the solution of this problem ( and one other ) were included in Niven's The Scientific Papers of James Clerk Maxwell, which was published eleven years after Maxwell's death.

Lorenz's work was the first symmetrizing shortening of Maxwell's equations after Maxwell himself published his 1865 paper.

In 1972, Maxwell's 15-year-old son arrived home from school and found her dead at the age of fifty of an apparent heart attack, after she had been treated for hypertension and pulmonary disease.

Toward the end of the 19th century, after James Clerk Maxwell's discoveries, it was clear that electric measurements could not be explained in terms of the three fundamental units of length, mass and time.