Maxwell's Equations/Ampère's Law with Maxwell's Addition
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Physical Law
- $\nabla \times \mathbf B = \mu_0 \paren {\mathbf J + \varepsilon_0 \dfrac {\partial \mathbf E} {\partial t} } $
where:
- $\nabla \times \mathbf B$ denotes the curl of the magnetic flux density $\mathbf B$
- $\mathbf J$ denotes the electric current
- $\mu_0$ denotes the vacuum permeability
- $\varepsilon_0$ denotes the vacuum permittivity
- $\dfrac {\partial \mathbf E} {\partial t}$ denotes the partial derivative of the electric field strength $\mathbf E$ with respect to time.
Also presented as
This equation can also be seen presented as:
- $\nabla \times \mathbf H = \mathbf J + \dfrac {\partial \mathbf D} {\partial t}$
where:
- $\mathbf D = \varepsilon_0 \mathbf E$ denotes the electric displacement field
- $\mathbf H = \dfrac 1 {\mu_0} \mathbf B$ denotes the magnetic field strength
Source of Name
This entry was named for James Clerk Maxwell and André-Marie Ampère.
Sources
- 1970: George Arfken: Mathematical Methods for Physicists (2nd ed.) ... (previous) ... (next): Introduction: Electromagnetic Theory