# Fundamental Physics/Electromagnetism/Electromagnetism Formulaes

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## Electric charge

 Electric charge Charge process Charge quantity Electric field Magnetic field Negative charge O + e -> - - Q -->E<-- B ↓ Positive charge O - e -> + + Q <--E--> B ↑

## Electric charge interaction force

 Electrostatic Force $F_{q}=K{\frac {q_{+}q_{-}}{d^{2}}}$ Electromotive Force $F_{E}=qE$ Electromagnetomotive Force $F_{B}=\pm qvB$ Electromagnetic Force $F_{EB}=F_{E}+F_{B}=qE\pm qvB=q(E\pm B)$ ## Electromagnet

 Configuration Magnetic Field Magnetic field intensity For a straight wire circular magnetic field surrounds a point charge along the straight line $B=LI={\frac {\mu }{2\pi r}}I$ For a circular loop circular magnetic field surrounds a point charge along the circular loop $B=LI={\frac {\mu }{2r}}I$ For a coil of N circular loops lines of magnetic field runs from North pole (Positive polarity) to South pole (Negative polarity) $B=LI={\frac {N\mu }{l}}I$ ## Electromagnetic induction

Electromagnetic induction takes place in a circular loop and a coil of N circular loops

$V={\frac {d}{dt}}B$ $\epsilon =-{\frac {d}{dt}}\phi$ For a single circular loop $B=LI={\frac {\mu }{2r}}I$ $V={\frac {dB}{dt}}=L{\frac {dI}{dt}}$ Coil of N circular loops $B=LI={\frac {N\mu }{l}}I$ $V={\frac {dB}{dt}}=L{\frac {dI}{dt}}$ $\phi =-NB=-NLI$ $\epsilon =-{\frac {d\phi }{dt}}=-N{\frac {dB}{dt}}=-NL{\frac {dI}{dt}}$ ## Electromagnetization

The way a coil of N circular loops turn metal inside the loops into a electromagnet describe by 4 vector equation below

$B=LI={\frac {N\mu }{l}}I$ $H={\frac {B}{\mu }}={\frac {NI}{l}}$ $\nabla \cdot D=\rho$ $\nabla \times E=-\nabla B$ $\nabla \cdot B=0$ $\nabla \times H=J+\nabla B$ ## Electromagnetic oscillation wave

The way a coil of N circular loops generates oscillation of 2 fields , Electric filed and Electromagnetic field , perpendicular to each other which can be expressed mathematically by 4 vector equations below

### Electromagnetic oscillation

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

Oscillation of Electromagnetic field and Electric field generates sinusoidal wave equations

$\nabla ^{2}E=-\omega E$ $\nabla ^{2}B=-\omega B$ ### Electromagnetic wave function

Solving equations above gives Electromagnetic sinusoidal wave function

$E=ASin\omega t$ $B=ASin\omega t$ $\omega ={\sqrt {\frac {1}{T}}}={\sqrt {\frac {1}{\mu \epsilon }}}=C=\lambda f$ $T=\mu \epsilon$ ## Electromagnetic wave radiation

### Electromagnetic wave radiation chracteristics

$v=\omega ={\sqrt {\frac {1}{\mu \epsilon }}}=C=\lambda f$ $E=pv=pC=p\lambda f=hf$ $h=p\lambda$ $p={\frac {h}{\lambda }}$ $\lambda ={\frac {h}{p}}={\frac {C}{f}}$ The following mathematical formulas can be derived

$E=hf=h{\frac {\omega }{2\pi }}=\hbar \omega$ $p={\frac {h}{\lambda }}=h{\frac {k}{2\pi }}=\hbar k$ $h=p\lambda ={\frac {E}{C}}\lambda =2\pi \hbar$ $\omega ={\frac {E}{\hbar }}$ $k={\frac {p}{\hbar }}$ $\hbar ={\frac {h}{2\pi }}={\frac {E}{\omega }}={\frac {p}{k}}$ ### Electromagnetic radiation's states

#### Electromagnetic Light Radiation

$v=\omega _{o}={\sqrt {\frac {1}{\mu _{o}\epsilon _{o}}}}=C=\lambda _{o}f$ $E=pv=pC=p\lambda _{o}f=hf_{o}$ $h=p\lambda _{o}$ $p={\frac {h}{\lambda _{o}}}$ $\lambda _{o}={\frac {h}{p}}={\frac {C}{f_{o}}}$ #### Electromagnetic Electricity Radiation

$v=\omega ={\sqrt {\frac {1}{\mu \epsilon }}}=C=\lambda f$ $E=pv=pC=p\lambda f=hf$ $h=p\lambda$ $p={\frac {h}{\lambda }}$ $\lambda ={\frac {h}{p}}={\frac {C}{f}}$ Photon (Electromagnetic wave radiation) exists in 2 states at specific frequency . .

#### Heinseiberg's uncertainty principle

States that

Photon cannot exist in 2 states at the same time


The chance to find one of its state (successful rate of finding photon) is 1/2 where h = p λ . h and p do not change, only wavelength changes with frequency

Mathematically, Uncertainty principle can be expressed as

$\Delta p\Delta \lambda ={\frac {1}{2}}{\frac {h}{2\pi }}={\frac {h}{4\pi }}={\frac {\hbar }{2}}$ 