23 Facts About Maxwell's equations

1.

The Maxwell's equations provide a mathematical model for electric, optical, and radio technologies, such as power generation, electric motors, wireless communication, lenses, radar etc.

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2.

The Maxwell's equations are named after the physicist and mathematician James Clerk Maxwell, who, in 1861 and 1862, published an early form of the Maxwell's equations that included the Lorentz force law.

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3.

Maxwell first used the Maxwell's equations to propose that light is an electromagnetic phenomenon.

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4.

The microscopic Maxwell's equations have universal applicability but are unwieldy for common calculations.

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5.

The macroscopic Maxwell's equations define two new auxiliary fields that describe the large-scale behaviour of matter without having to consider atomic-scale charges and quantum phenomena like spins.

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Lorentz force Planck's law
6.

The term "Maxwell's equations" is often used for equivalent alternative formulations.

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7.

Versions of Maxwell's equations based on the electric and magnetic scalar potentials are preferred for explicitly solving the equations as a boundary value problem, analytical mechanics, or for use in quantum mechanics.

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8.

Publication of the Maxwell's equations marked the unification of a theory for previously separately described phenomena: magnetism, electricity, light, and associated radiation.

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9.

Since the mid-20th century, it has been understood that Maxwell's equations do not give an exact description of electromagnetic phenomena, but are instead a classical limit of the more precise theory of quantum electrodynamics.

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10.

Maxwell's equations explain how these waves can physically propagate through space.

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11.

Above equations are the microscopic version of Maxwell's equations, expressing the electric and the magnetic fields in terms of the charges and currents present.

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12.

Cost of this splitting is that the additional fields and need to be determined through phenomenological constituent Maxwell's equations relating these fields to the electric field and the magnetic field, together with the bound charge and current.

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13.

An alternative viewpoint on the microscopic Maxwell's equations is that they are the macroscopic Maxwell's equations together with the statement that vacuum behaves like a perfect linear "material" without additional polarization and magnetization.

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14.

Maxwell Maxwell's equations can be formulated on a spacetime-like Minkowski space where space and time are treated on equal footing.

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15.

Maxwell's equations are partial differential equations that relate the electric and magnetic fields to each other and to the electric charges and currents.

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16.

In some cases, Maxwell's equations are solved over the whole of space, and boundary conditions are given as asymptotic limits at infinity.

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17.

In other cases, Maxwell's equations are solved in a finite region of space, with appropriate conditions on the boundary of that region, for example an artificial absorbing boundary representing the rest of the universe, or periodic boundary conditions, or walls that isolate a small region from the outside world .

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18.

However, Jefimenko's Maxwell's equations are unhelpful in situations when the charges and currents are themselves affected by the fields they create.

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19.

Maxwell's equations seem overdetermined, in that they involve six unknowns but eight equations .

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20.

Maxwell's equations are thought of as the classical limit of quantum electrodynamics .

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21.

The approximate nature of Maxwell's equations becomes more and more apparent when going into the extremely strong field regime or to extremely small distances.

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22.

Finally, Maxwell's equations cannot explain any phenomenon involving individual photons interacting with quantum matter, such as the photoelectric effect, Planck's law, the Duane–Hunt law, and single-photon light detectors.

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23.

Maxwell's equations posit that there is electric charge, but no magnetic charge, in the universe.

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