# Alternative Forms of Maxwell's Equations

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To anyone versed in science, the immense range of physical phenomena that can be encoded in Maxwell’s four relatively compact equations is breathtaking. Added to this is the remarkable symmetry between electric and magnetic variables and the fundamental underlying symmetry inherent in the special theory of relativity. One suggested measure of elegance is whether the equations can fit nicely on a T-shirt.

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Contributed by: S. M. Blinder (September 2018)

Open content licensed under CC BY-NC-SA

## Details

Key to symbols:

electric field,

magnetic induction,

electric displacement,

magnetic field,

charge density,

current density,

vacuum permittivity,

vacuum permeability,

speed of light,

vector potential,

scalar potential,

4-potential,

4-current,

d’Alembertian operator,

,

,

electromagnetic field tensor,

Levi–Civita symbol.

In spacetime algebra:

,

,

.

References

[1] Wikipedia. "Maxwell's Equations." (Aug 27, 2018) en.wikipedia.org/wiki/Maxwell%27 s_equations.

[2] Wikipedia. "Electromagnetic Four-Potential." (Aug 27, 2018) en.wikipedia.org/wiki/Electromagnetic_four-potential.

[3] Wikipedia. "Covariant Formulation of Classical Electromagnetism." (Aug 27, 2018) en.wikipedia.org/wiki/Covariant_formulation_of _classical _electromagnetism.

[4] Wikipedia. "Mathematical Descriptions of the Electromagnetic Field." (Aug 27, 2018) en.wikipedia.org/wiki/Mathematical_descriptions_of _the _electromagnetic _field.

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## Permanent Citation