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Differential Form of Maxwell Equation

#### Gauss’s law

$$div {\bf D}({\bf r},t)=ρ({\bf r},t)$$

#### Law of the magnetic flux conservation

$$div {\bf B}({\bf r},t)=0$$

#### Maxwell-Ampere law

$$rot {\bf H}({\bf r},t)={\bf i}({\bf r},t)+\frac{∂{\bf D}({\bf r},t)}{∂t}$$

#### Faraday’s law of induction

$$rot {\bf E}({\bf r},t)=-\frac{∂{\bf B}({\bf r},t)}{∂t}$$

Relation between electric field and electric flux density, magnetic field and magnetic flux density

$${\bf D}({\bf r},t)=ε{\bf E}({\bf r},t)$$

$${\bf B}({\bf r},t)=μ{\bf H}({\bf r},t)$$

\({\bf E}({\bf r},t)\):Electric field \({\bf D}({\bf r},t)\):Electric flux density \({\bf H}({\bf r},t)\):Magnetic field \({\bf B}({\bf r},t)\):Magnetic flux density

\(ρ({\bf r},t)\):Charge density \({\bf i}({\bf r},t)\):Current density \(ε\):Dielectric constant (Dielectric) \(μ\):Magnetic permeability (Permeability)

The first four equations are collectively called the Maxwell equation. The form is called **the differential form of the Maxwell equation**. The latter two supplements wrote the electric field and electric flux density, and the relational expressions of the magnetic field and the magnetic flux density, respectively.

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