# Electromagnetism

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At university we often think of series RLC circuits. L is a coil, R is a resistance, and C is a capacitor. The relationship between the voltage applied to each electronic component and the current is given as follows.

#### Voltage of Coil $V_L$

$$V_{L}(t)=L\frac{dI(t)}{dt}$$

#### Voltage of Resistance $V_R$

$$V_{R}(t)=RI(t)$$

#### Voltage of Capacitor $V_C$

$$V_{C}(t)=\frac{1}{C} \int I(t) dt=\frac{Q(t)}{C}$$

$L$:Self-inductance of the coil　$R$:Resistance   $C$:Capacitance   $Q(t)$:Charge stored in the capacitor

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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

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

$$rot {\bf E}({\bf r},t)=-\frac{∂{\bf B}({\bf r},t)}{∂t}$$
$${\bf D}({\bf r},t)=ε{\bf E}({\bf r},t)$$
$${\bf B}({\bf r},t)=μ{\bf H}({\bf r},t)$$
${\bf E}({\bf r},t)$: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)