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Maxwell's Equations

(four equations describing electricity and magnetism)

Maxwell's Equations are four equations that James Clerk Maxwell created and/or refined that describe the behavior and interaction of electricity and magnetism. This description includes the conditions for propagating waves, i.e., Electromagnetic waves, explaining Electromagnetic Radiation, including Visible Light.

The equations are (in their differential-equation form):

Gauss's Law ∇ · E = 4πρ Electric field lines begin and end at charged particles.
Gauss's Law For Magnetism ∇ · B = 0 Magnetic Field lines don't end: they form circuits.
If Magnetic Monopoles existed, a non-zero value could be on the right side of this equation.
Maxwell-Faraday Equation ∇ × E = - (1/c) ∂B/∂t The magnetic field is shifting when/where the electric field curls around.
Ampere's Law ∇ × B = (1/c)(4πJ + ∂E/∂t) When/where the magnetic field curls around, you get electric current, or a shift in the electric field, or some of each.
  • E - electric field.
  • B - magnetic field (Magnetic Flux Density).
  • J - electric current density.
  • ρ - electric charge density.
  • t - time.
  • c - speed of light.


Referenced by:
CMB Polarization
Coulomb's Law
Lorentz Force
Magnetic Flux Density (B)
Magnetic Induction
Magnetohydrodynamics (MHD)
Mie Scattering
Telegrapher's Equations