Fundamental Physics/Electricity/Electromagnetism

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Electric charge

Electric charge is refered to matter that carries electricity . In natural state, all matter is neutral in charge . When matter gives or receives electron (negatively charged particle) , matter becomes electric charge . Static electricity the process matter acquires charged particle (electron) to become electric charge . Matter receives electron will become negative electric charge . Matter gives electron will become positive electric charge

Matter + e- -- > Negative Charge (-)
Matter - e- -- > Positive Charge (+)

Electric charge properties

Charge Quantity

Electric charge has a symbol Q measured in Coulomb unit C . One coulomb charge contains N-m . Positive electric charge has symbol +Q carries +1C . Negative electric charge has symbol +Q carries +1C

${\displaystyle 1C=}$

Electric Field

All electric charge process electric field lines pointing inward or outward . For negative charge, the electric field lines point inward . For positive charge, the electric field lines point outward.

Negative Charge . Positive Charge

Magnetic Field

All charge process circular magnetic field lines point inward or outward surround charge . For negative charge, the electric field lines point inward . For positive charge, the electric field lines point outward.

Negative Charge . B ↑
Positive Charge . B ↓

Interaction of electric charge

Electric charges interaction

Coulomb discovered that charges of the same polaities will repulse . Charges of different polarities will attract . Negative charge will attract positive charge . The force of attraction is called Electrostatic force or Coulomb force . Electrostatic force has a symbol FQ measured in unit Newton N

Electrostatic force or Coulomb force is used in calculating the force of negative charge attracts positive charge

${\displaystyle F_{Q}={\frac {|Q_{+}||Q_{-}|}{r^{2}}}}$

Electric charge and electricity interaction

Ampere discovered that, electricity exerts a force to force electric charge to move in a linear path will create a field of electric lines called Electric field . This force is called Electrodynamic force or Ampere force which has a symbol FE measured in unit Newton N

${\displaystyle F_{E}=QE}$

Electric charge and magnet interaction

Lorentz discovered that when electric charge travels through a magnet, magnet exerts a force to deflect

${\displaystyle F_{B}=\pm QvB}$

Electromagnetic Force

 Electrostatic force ${\displaystyle F_{q}}$ ${\displaystyle K{\frac {q_{+}q_{-}}{r^{2}}}}$ Electrodynamic force ${\displaystyle F_{E}}$ ${\displaystyle qE}$ Electromagnetomotive force ${\displaystyle F_{B}}$ ${\displaystyle \pm qvB}$ Electromagnetic force ${\displaystyle F_{EB}}$ ${\displaystyle qE\pm qvB=q(E\pm vB)}$

Electromagnetic field

Electromagnetic field

Experiment has shown that non zero current flows inside conductor generates magnetic field around conductor

 Straight line conductor Magnetic field is made of circular loops around straight line conductor Circular loop conductor Magnetic field is made of circular loops around a point charge on the circle Coil of N circular loops Magnetic field is made of eleptic loops run from north pole to south pole

Electromagnetic field's strength

The strength of magnetic field can be calculated by Ampere's law as follow

${\displaystyle B=Li}$
 Straight line conductor ${\displaystyle B=Li={\frac {\mu }{2\pi r}}i}$ Circular loop conductor ${\displaystyle B=Li={\frac {\mu }{2r}}i}$ Coil of N circular loops ${\displaystyle B=Li={\frac {N\mu }{l}}i}$

Electromagnetic induction

Electromagnetic induction is found by Lorentz and Faraday

Lorentz's electromagnetic induction

${\displaystyle V={\frac {dB}{dt}}}$

${\displaystyle -\epsilon =-{\frac {d\phi }{dt}}}$

 Circular loop ${\displaystyle B=Li={\frac {\mu }{2r}}i}$${\displaystyle V={\frac {d}{dt}}B=L{\frac {di}{dt}}}$ Coil of N circular loops ${\displaystyle B=Li={\frac {N\mu }{l}}i}$${\displaystyle V={\frac {d}{dt}}B=L{\frac {di}{dt}}}$${\displaystyle \phi =-NB=-NLi}$${\displaystyle -\epsilon =-{\frac {d\phi }{dt}}=-L{\frac {dB}{dt}}=-NL{\frac {di}{dt}}}$

Electromagnetization

 Permanent Electromagnet Field ${\displaystyle H={\frac {B}{\mu }}={\frac {Ni}{l}}}$ Vector equations ${\displaystyle \nabla \cdot D=\rho }$${\displaystyle \nabla \times E=-{\frac {\partial }{\partial t}}B}$${\displaystyle \nabla \cdot B=0}$${\displaystyle \nabla \times H=J+{\frac {\partial }{\partial t}}B}$

Electromagnetic oscillation wave

 A coil of N circular loops Electromagnetic oscillation vector equations ${\displaystyle \nabla \cdot E=0}$${\displaystyle \nabla \times E={\frac {1}{T}}E}$${\displaystyle \nabla \cdot B=0}$${\displaystyle \nabla \times B={\frac {1}{T}}E}$ Electromagnetic wave's equations ${\displaystyle \nabla ^{2}E=-\omega E}$${\displaystyle \nabla ^{2}B=-\omega B}$ Electromagnetic wave's function ${\displaystyle E=ASin\omega t}$${\displaystyle B=ASin\omega t}$${\displaystyle \omega ={\sqrt {\frac {1}{T}}}=C={\sqrt {\frac {1}{\mu \epsilon }}}=\lambda f}$${\displaystyle T=\mu \epsilon }$

 Electromagnetic wave radiation ${\displaystyle v=\omega ={\sqrt {\frac {1}{T}}}=C={\sqrt {\frac {1}{\mu \epsilon }}}=\lambda f}$${\displaystyle E=pv=pC=p\lambda f=hf}$${\displaystyle h=p\lambda }$${\displaystyle p={\frac {h}{\lambda }}}$${\displaystyle \lambda ={\frac {h}{p}}}$ Quatization ${\displaystyle h=p\lambda ={\frac {E}{f}}}$ Wave particle duality Wave like . ${\displaystyle \lambda ={\frac {h}{p}}}$Particle like . ${\displaystyle p={\frac {h}{\lambda }}}$ Photon's state Radiant photon ${\displaystyle E_{o}=hf_{o}=h{\frac {C}{\lambda _{o}}}}$Non radiant photon${\displaystyle E=hf=h{\frac {C}{\lambda }}}$ Heinsberg's uncertainty principle ${\displaystyle \Delta \lambda \Delta p={\frac {1}{2}}{\frac {h}{2\pi }}={\frac {h}{4\pi }}={\frac {\hbar }{2\pi }}}$

 Configuration Straight line conductor Coil conductor Coil conductor Magnetic field's strength ${\displaystyle B={\frac {\mu }{2\pi r}}}$ ${\displaystyle B={\frac {N\mu _{o}}{l}}}$ ${\displaystyle B={\frac {N\mu }{l}}}$ Radiation condition ${\displaystyle R(T)=R_{o}+nT}$ ${\displaystyle R(T)=R_{o}e^{nT}}$ ${\displaystyle v=C=\lambda _{o}f_{o}}$ ${\displaystyle v=C=\lambda f}$ Radiation's energy ${\displaystyle E_{R}=i^{2}R(T)=mC\Delta T}$ ${\displaystyle E_{o}=hf_{o}}$ ${\displaystyle E=hf}$ Matter's quantity ${\displaystyle m={\frac {E_{R}}{C\Delta T}}}$ ${\displaystyle h=p\lambda _{o}}$ ${\displaystyle h=p\lambda }$ Matter's wave ${\displaystyle \lambda _{o}={\frac {h}{p}}}$ ${\displaystyle \lambda ={\frac {h}{p}}}$ Matter's momentum ${\displaystyle p={\frac {h}{\lambda _{o}}}}$ ${\displaystyle p={\frac {h}{\lambda }}}$ Photon state uncertainty ${\displaystyle \Delta \lambda p={\frac {1}{2}}{\frac {h}{2\pi }}}$ ${\displaystyle \Delta \lambda p={\frac {h}{4\pi }}={\frac {\hbar }{2}}}$ Frequency spectrum ${\displaystyle f ${\displaystyle f=f_{o}}$ ${\displaystyle f>f_{o}}$ Frequency range RF , uF , IF VF UVF , X , G

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

 Frequency spectrum Characteristics Radio wave , RF Microwave , uF Infrared , IF Visible light , VF Ultraviolet light , UVF X ray, X Gamma ray, G

Heat transfer

 Heat transfer Heat conduction Heat convection Heat radiation Condition ${\displaystyle \Delta T=T_{1}-T_{0}}$ ${\displaystyle v=\omega _{o}}$ ${\displaystyle v=\omega }$ Energy ${\displaystyle E=mC\Delta T}$ ${\displaystyle E=hf_{o}}$ ${\displaystyle E=hf}$ Matter's quantity ${\displaystyle m={\frac {E}{C\Delta T}}}$ ${\displaystyle h=p\lambda _{o}={\frac {E}{f_{o}}}}$ ${\displaystyle h=p\lambda ={\frac {E}{f}}}$

 Matter decay Alpha decay Beta decay Gamma decay Radiation's speed ${\displaystyle \gamma }$ ${\displaystyle v=\omega _{o}={\sqrt {\frac {1}{\mu _{o}\epsilon _{o}}}}=C=\lambda _{o}f_{o}}$ ${\displaystyle v=\omega ={\sqrt {\frac {1}{\mu \epsilon }}}=C=\lambda f}$ Radiation's matter quantity ${\displaystyle M=m_{o}(\gamma -1)}$ ${\displaystyle h=p\lambda _{o}={\frac {E}{f_{o}}}}$ ${\displaystyle h=p\lambda ={\frac {E}{f}}}$ Energy ${\displaystyle E=M\gamma ^{2}}$ ${\displaystyle E=hf_{o}}$ ${\displaystyle E=hf}$ Momentum ${\displaystyle p=M\gamma }$ ${\displaystyle p={\frac {h}{\lambda _{o}}}}$ ${\displaystyle p={\frac {h}{\lambda }}}$ Wavelength ${\displaystyle \lambda _{o}={\frac {h}{p}}={\frac {C}{f_{o}}}}$ ${\displaystyle \lambda ={\frac {h}{p}}={\frac {C}{f}}}$

Applications

Electromagnets

Electromagnets are very widely used in electric and electromechanical devices, including: