Maxwell's Equations/Gauss's Law

Physical Law

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

where:

$\nabla \cdot \mathbf D$ denotes the divergence of the electric displacement field $\mathbf D$

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

$\rho$ denotes electric charge density

$\mathbf E$ denotes the electric field $\mathbf E$

$\varepsilon_0$ denotes the vacuum permittivity.

Also presented as

Gauss's law can also be seen presented as:

$\nabla \cdot \mathbf E = \dfrac \rho {\varepsilon_0}$

where:

$\nabla \cdot \mathbf E$ denotes the divergence of the electric field $\mathbf E$

$\rho$ denotes electric charge density

$\varepsilon_0$ denotes the vacuum permittivity.

Also see

• Maxwell's Equations

Source of Name

This entry was named for James Clerk Maxwell and Carl Friedrich Gauss.

Sources

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