Maxwell's Equations

Physical Laws

Gauss's Law

$\nabla \cdot \mathbf D = \rho$

Gauss's Law for Magnetism

$\nabla \cdot \mathbf B = 0$

Maxwell-Faraday Equation

$\nabla \times \mathbf E = -\dfrac {\partial \mathbf B} {\partial t}$

Ampère's Law with Maxwell's Addition

$\nabla \times \mathbf B = \mu_0 \paren {\mathbf J + \varepsilon_0 \dfrac {\partial \mathbf E} {\partial t} } $

where:

$\nabla \cdot$ denotes the divergence operator

$\nabla \times$ denotes the curl operator

$\dfrac \partial {\partial t}$ denotes the partial derivative with respect to time.

$\mathbf D = \varepsilon_0 \mathbf E$ denotes the electric displacement field

$\mathbf E$ denotes the electric field strength

$\mathbf B$ denotes the magnetic flux density

$\mathbf J$ denotes the electric current

$\rho$ denotes electric charge density

$\varepsilon_0$ denotes the vacuum permittivity

$\mu_0$ denotes the vacuum permeability.

Also known as

Maxwell's equations are also known as Maxwell's laws.

Source of Name

This entry was named for James Clerk Maxwell.

Sources

• 1970: George Arfken: Mathematical Methods for Physicists (2nd ed.) ... (next): Introduction: Electromagnetic Theory
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Maxwell's equations
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Maxwell's equations