Electromagnetic wave

Electromagnetic wave
Electromagnetic waves are synchronized oscillations of electric and magnetic fields that propagate at the speed of light through a vacuum. The oscillations of the two fields are perpendicular to each other and perpendicular to the direction of energy and wave propagation, forming a transverse wave.

Electromagnetic waves are produced whenever charged particles are accelerated, and these waves can subsequently interact with other charged particles.
 * Onde electromagnetique.svg

Vector equation of Electromagnetic wave
 * $$\nabla \cdot E = 0$$
 * $$\nabla \times E = \frac{1}{T} E$$
 * $$\nabla \cdot B = 0$$
 * $$\nabla \times B = \frac{1}{T} B$$

Electromagnetic wave equation
 * $$\nabla^2 E = -\omega E$$
 * $$\nabla^2 B = -\omega B$$

Electromagnetic wave function
 * $$ E = A Sin \omega t$$
 * $$ B = A Sin \omega t$$
 * $$\omega = \sqrt{\frac{1}{T}} = C = \lambda f$$
 * $$T = \mu \epsilon$$

Electromagnetic radiation
Electromagnetic radiation is associated with those EM waves that are free to propagate themselves ("radiate") without the continuing influence of the moving charges that produced them, because they have achieved sufficient distance from those charges. Thus, EMR is sometimes referred to as the far field. In this language, the near field refers to EM fields near the charges and current that directly produced them, specifically, electromagnetic induction and electrostatic induction phenomena.

EM waves carry energy, momentum and angular momentum away from their source particle and can impart those quantities to matter with which they interact. Quanta of EM waves are called photons, whose rest mass is zero, but whose energy, or equivalent total (relativistic) mass, is not zero so they are still affected by gravity.

Electromagnetic radiation travels as a moment at speed
 * $$v = \omega = \sqrt{\frac{1}{T}} = C = \lambda f$$

Carry energy level
 * $$E = p v = p C = p \lambda f = h f$$

Where
 * $$h = p \lambda$$

From above
 * $$p = \frac{h}{\lambda}$$
 * $$\lambda = \frac{h}{p} = \frac{C}{f}$$

Electromagnetic radiation is in the form of a Quanta,  h  , whose rest mass is zero. EM travels as Electromagnetic wave at speed of light carries an energy level of a Photon, hf


 * Photon (Quanta's energy) . $$E_h = hf = h (\frac{\omega}{2 \pi}) =\hbar \omega$$
 * Quanta (Massless particle) . $$h = p \lambda$$
 * Moment. $$p = \frac{h}{\lambda} = h \frac{k}{2 \pi} = \hbar k$$

Electromagnetic spectrum
The wavefront of electromagnetic waves emitted from a point source (such as a lightbulb) is a sphere. The position of an electromagnetic wave within the electromagnetic spectrum could be characterized by either its frequency of oscillation or its wavelength

The Electromagnetic spectrum includes, in order of increasing frequency and decreasing wavelength:


 * radio waves,
 * microwaves,
 * infrared radiation,
 * visible light,
 * ultraviolet radiation,
 * X-rays
 * gamma rays

Electromagnetic radiation quantization
Electromagnetic radiation carries an energy level
 * $$E= pv = pC = p \lambda f = h f$$

This energy is quantized by a quantity called quanta
 * $$h = p \lambda$$

Electromagnetic radiation dualitty
Electromagnetic radiation carries an energy level
 * $$E= h f$$

This energy is quantized by a quantity called quanta
 * $$h = p \lambda$$

Which displays a duality of Wave-Particle like
 * Wave like . $$\lambda = \frac{h}{p}$$
 * Particle like . $$p = \frac{h}{\lambda}$$

Electromagnetic radiation state
There are two states that photon are found Radiant Photon and Electric Photon

Radiant Photon is found at threshold frequency, fo
 * $$f = f_o = \frac{C}{\lambda_o}$$
 * $$E = hf_o $$
 * $$h = p \lambda_o$$
 * $$p = \frac{h}{\lambda_o} $$
 * $$\lambda_o = \frac{h}{p} = \frac{C}{f_o} $$

Electric Photon is found at frequency greater than the threshold frequency, f > fo
 * $$f > f_o > \frac{C}{\lambda_o}$$
 * $$E = hf $$
 * $$h = p \lambda$$
 * $$p = \frac{h}{\lambda} $$
 * $$\lambda_o = \frac{h}{p} = \frac{C}{f} $$

Photon cannot exist in 2 states at the same time
 * $$\Delta p \Delta \lambda > \frac{1}{2} \frac{h}{2 \pi} = \frac{h}{4 \pi}= \frac{\hbar}{2}$$

Electromagnetic radiation and matter

 * EM Spectrum Properties edit.svg

Penetration
Radiant photon (Beta photon) does not penetrate into matter. Electric photon (Gamma photon) penetrates into matter to create heat transfer in matter and can free electron from matter's substances' atom according to Photoelectric effect

Deflection
Photon enters a magnetic field will be deflected
 * Alpha photon will be deflected upward
 * Beta photon will be not be deflected and travel straight
 * Gamma photon will be deflected downward

Reference

 * Electromagnetic radiation