Maxwell's equations

∇×E=−∂B∂t\bm\nabla\times \bm E = -\frac{\partial\bm B}{\partial t}
∇×H=J+∂D∂t\bm\nabla\times \bm H = \bm J + \frac{\partial \bm D}{\partial t}
∇⋅D=ρ\bm \nabla\cdot D = \rho
∇B=0\bm\nabla\bm B = 0

The Conservation Equation

∇⋅J+∂ρ∂t=0\bm \nabla\cdot\bm J + \frac{\partial\rho}{\partial t} = 0

Potentials

V(r,t)=14πϵ0∫ρ(r′,t−Rc)R dv′=14πϵ0∫ρretR dv′V(\bm r, t) = \frac 1{4\pi\epsilon_0}\int\frac{\rho\left(\bm r', t-\frac Rc\right)}{R}\: dv' = \frac 1{4\pi\epsilon_0}\int\frac{\rho_{ret}}R\: dv'
A(r,t)=μ04π∫J(r′,t−Rc)R dv′=μ04π∫JretR dv′\bm A(\bm r, t) = \frac{\mu_0}{4\pi}\int\frac{\bm J\left(\bm r', t - \frac Rc\right)}R\: dv' = \frac{\mu_0}{4\pi}\int\frac{\bm J_{ret}}R\: dv'
B=∇×A\bm B = \bm\nabla\times\bm A
E=−∇V−∂A∂t\bm E = -\bm\nabla V - \frac{\partial \bm A}{\partial t}

Magnetic Flow Density

B(r,t)=μ04π∫Jret×eRR2 dv′+μ04πc∫Jret′×eRR dv′\bm B(\bm r, t) = \frac{\mu_0}{4\pi}\int \frac{\bm J_{ret}\times\bm e_R}{R^2}\: dv' + \frac{\mu_0}{4\pi c}\int\frac{\bm J'_{ret}\times \bm e_R}{R}\: dv'

Filamentuos Antenna

B=μ04π∫i(z,t−R/c)dl×eRR2+μ04πc∫i(z,t−R/c)dl×eRR\bm B = \frac{\mu_0}{4\pi}\int \frac{i(z, t - R/c)d\bm l\times\bm e_R}{R^2} + \frac{\mu_0}{4\pi c}\int\frac{i(z, t - R/c)d\bm l\times \bm e_R}{R}

Oscillating Electric Dipole

B=μ04πp′(t−R/c)×eRR2+μ04πcp′′(t−R/c)×eRR\bm B = \frac{\mu_0}{4\pi} \frac{\bm p'(t - R/c)\times\bm e_R}{R^2} + \frac{\mu_0}{4\pi c}\frac{\bm p''(t - R/c)\times\bm e_R}R

Oscillating Magnetic Dipole

B=−μ04πm′(t−R/c)×eRR2−μ04πcm′′(t−R/c)×eRR\bm B = -\frac{\mu_0}{4\pi} \frac{\bm m'(t - R/c)\times\bm e_R}{R^2} - \frac{\mu_0}{4\pi c}\frac{\bm m''(t - R/c)\times\bm e_R}R

Pointing's Vector

PS(r,t)=E(r,t)×H(r,t)\bm P_S(\bm r, t) = \bm E(\bm r, t)\times\bm H(\bm r, t)