Electromagnetic wave

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## Electromagnetic wave

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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.

Vector equation of Electromagnetic wave

∇ ⋅ E = 0 {\displaystyle \nabla \cdot E=0}
∇ × E = 1 T E {\displaystyle \nabla \times E={\frac {1}{T}}E}
∇ ⋅ B = 0 {\displaystyle \nabla \cdot B=0}
∇ × B = 1 T B {\displaystyle \nabla \times B={\frac {1}{T}}B}

Electromagnetic wave equation

∇ 2 E = − ω E {\displaystyle \nabla ^{2}E=-\omega E}
∇ 2 B = − ω B {\displaystyle \nabla ^{2}B=-\omega B}

Electromagnetic wave function

E = A S i n ω t {\displaystyle E=ASin\omega t}
B = A S i n ω t {\displaystyle B=ASin\omega t}
ω = 1 T = C = λ f {\displaystyle \omega ={\sqrt {\frac {1}{T}}}=C=\lambda f}
T = μ ϵ {\displaystyle T=\mu \epsilon }

## Electromagnetic radiation

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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 = ω = 1 T = C = λ f {\displaystyle v=\omega ={\sqrt {\frac {1}{T}}}=C=\lambda f}

Carry energy level

E = p v = p C = p λ f = h f {\displaystyle E=pv=pC=p\lambda f=hf}

Where

h = p λ {\displaystyle h=p\lambda }

From above

p = h λ {\displaystyle p={\frac {h}{\lambda }}}
λ = h p = C f {\displaystyle \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 = h f = h ( ω 2 π ) = ℏ ω {\displaystyle E_{h}=hf=h({\frac {\omega }{2\pi }})=\hbar \omega }
Quanta (Massless particle) .  h = p λ {\displaystyle h=p\lambda }
Moment.  p = h λ = h k 2 π = ℏ k {\displaystyle p={\frac {h}{\lambda }}=h{\frac {k}{2\pi }}=\hbar k}

### Electromagnetic spectrum

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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

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Electromagnetic radiation carries an energy level

E = p v = p C = p λ f = h f {\displaystyle E=pv=pC=p\lambda f=hf}

This energy is quantized by a quantity called quanta

h = p λ {\displaystyle h=p\lambda }

### Electromagnetic radiation dualitty

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Electromagnetic radiation carries an energy level

E = h f {\displaystyle E=hf}

This energy is quantized by a quantity called quanta

h = p λ {\displaystyle h=p\lambda }

Which displays a duality of Wave-Particle like

Wave like .  λ = h p {\displaystyle \lambda ={\frac {h}{p}}}
Particle like .  p = h λ {\displaystyle p={\frac {h}{\lambda }}}

### Electromagnetic radiation state

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There are two states that photon are found Radiant Photon and Electric Photon

Radiant Photon is found at threshold frequency , fo

f = f o = C λ o {\displaystyle f=f_{o}={\frac {C}{\lambda _{o}}}}
E = h f o {\displaystyle E=hf_{o}}
h = p λ o {\displaystyle h=p\lambda _{o}}
p = h λ o {\displaystyle p={\frac {h}{\lambda _{o}}}}
λ o = h p = C f o {\displaystyle \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 > C λ o {\displaystyle f>f_{o}>{\frac {C}{\lambda _{o}}}}
E = h f {\displaystyle E=hf}
h = p λ {\displaystyle h=p\lambda }
p = h λ {\displaystyle p={\frac {h}{\lambda }}}
λ o = h p = C f {\displaystyle \lambda _{o}={\frac {h}{p}}={\frac {C}{f}}}

Photon cannot exist in 2 states at the same time

Δ p Δ λ > 1 2 h 2 π = h 4 π = ℏ 2 {\displaystyle \Delta p\Delta \lambda >{\frac {1}{2}}{\frac {h}{2\pi }}={\frac {h}{4\pi }}={\frac {\hbar }{2}}}

## Electromagnetic radiation and matter

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#### Penetration

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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

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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

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* Wikipedia: Electromagnetic radiation