Current Density

I=∫J⋅en dSI = \int \bm J \cdot e_n\: dS

Conservation Equation

Δ⋅J+∂ρ∂t=0\bm\Delta\cdot\bm J + \frac{\partial\rho}{\partial t} = 0
∮J⋅en dS=−dQdt\oint\bm J\cdot\bm e_n\: dS = -\frac{dQ}{dt}

Conductivity

J=σE\bm J = \sigma \bm E

Effect

P=∫J⋅E dvP = \int \bm J\cdot\bm E\: dv

Boundary Conditions

{en2⋅(J1−J2)=0(no surface current)Et1=Et2\begin{cases} \bm e_{n2}\cdot(\bm J_1 - \bm J_2) = 0 \quad \textup{(no surface current)} \\ \bm E_{t1} = \bm E_{t2} \end{cases}

Time Constant

RC=ϵrϵ0σRC = \frac{\epsilon_r\epsilon_0}{\sigma}

Analogy Elektrostatics - DC Current

E,VE,VDJϵrϵ0σQICG\def\arraystretch{1.5} \begin{array}{|c|c|} \hline \bm E, V & \bm E, V \\ \bm D & \bm J \\ \epsilon_r\epsilon_0 & \sigma \\ Q & I \\ C & G \\ \hline \end{array}