Maxwell's Equations
(Redirected from Definition:Maxwell's Equations)
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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