Maxwell’s Equations:

• $\oint E \cdot d A=Q / \varepsilon_{0}$ (Gauss’s Law for electricity)

• $\oint \mathrm{B} \cdot \mathrm{dA}=0$ (Gauss’s Law for magnetism)

• $\oint \mathrm{E} \cdot \mathrm{d} \ell=\frac{-\mathrm{d} \Phi_{\mathrm{B}}}{\mathrm{dt}}$ (Faraday’s Law)

• $\oint B \cdot d \ell=\mu_{0} i_{c}+\mu_{0} \varepsilon_{0} \frac{d \Phi_{E}}{dt}$ (Ampere-Maxwell Law)

Oscillating Electric And Magnetic Fields:

$$E=E_{x}(t)=E_{0} \sin (k z-\omega t)$$

$$=E_{0} \sin \left[2 \pi\left(\frac{z}{\lambda}-v t\right)\right]=E_{0} \sin \left[2 \pi\left(\frac{z}{\lambda}-\frac{t}{T}\right)\right]$$

$$E_{0} / B_{0}=c$$

where:

• $c=1 / \sqrt{\mu_{0} \varepsilon_{0}} \quad c$ is speed of light in vacuum

• $v=1 / \sqrt{\mu \varepsilon} \quad v$ is speed of light in medium

• $p=\frac{U}{c}$ energy transferred to a surface in time $t$ is $U$, the magnitude of the total momentum delivered to this surface (for complete absorption) is $p$

Relation Between The Magnetic Field Vector And The Electric Field Vector:

$$\vec{B} = \frac{1}{\omega}(\vec{k} \times \vec{E})$$

Wave Velocity:

The relationship between the speed of light (c), the angular frequency $( \omega)$, and the wave number k: $$c = \frac{\omega}{k}$$

Poynting vector:

$$\vec{S} = \frac{1}{c}(\vec{E} \times \vec{B})$$

Electromagnetic Spectrum: