# Fundamental Physics/Electromagnetism

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It is necessary to revise the following mathematical concepts as they are used throughout this course:

## Electrostatics

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
Coulomb law . Like charges repel, different charges attract . Negative charge attracts positive charge . The force of attraction negative charge attracts positive charge is called Electrostatic force can be calculated by Coulomb law as follow
${\displaystyle F_{Q}=K{\frac {Q_{+}Q_{-}}{r^{2}}}}$
Ampere law . The force that sets electric charge in motion from stationary state is called Electromotive force can be calculated by Ampere law as follow
${\displaystyle F_{Q}=QE}$
Lorentz law . When electric charge interacts with magnetic field of a magnet, the magnetic force of the magnet will make electric charge to move perpendicular to the initial moving direction . The positive charge will move up, the negative charge will move down . The force of magnetic field that sets electric charge to move perpendicular to the intial moving direction is called Electromagnetomotive force can be calculated as follow
${\displaystyle F_{B}=\pm QvB}$
The sum of 2 forces Electromotive force and Electromagnetomotive force creates Electromagnetic force
${\displaystyle F_{EB}=F_{E}+F_{B}=QE\pm QvB=Q(E\pm vB)}$

Electrostatic field

The force of attraction of 2 different charges

${\displaystyle F=K{\frac {Q_{-}Q_{+}}{r^{2}}}=K{\frac {Q^{2}}{r^{2}}}}$ . ${\displaystyle Q_{-}=Q+}$

The electric field of the charge in motion

${\displaystyle E={\frac {F}{Q}}={\frac {Q}{r^{2}}}}$

Electric Potential

The potential of the electric field

${\displaystyle V=\int Edr={\frac {Q}{r}}}$

## Magnetostatics

${\displaystyle F_{Q}={\frac {Q_{+}Q_{-}}{r^{2}}}}$
${\displaystyle \Phi =\oint _{S}\mathbf {E} \cdot d\mathbf {S} ={\frac {q_{in}}{\varepsilon _{0}}}}$
${\displaystyle \mathbf {B} (\mathbf {r} )={\frac {\mu _{0}}{4\pi }}\int _{C}{\frac {Id\mathbf {l} \times \mathbf {r'} }{|\mathbf {r'} |^{3}}}}$
${\displaystyle B=Li}$
${\displaystyle \phi =-B}$
${\displaystyle V={\frac {d}{dt}}B=L{\frac {d}{dt}}i}$
${\displaystyle F_{B}=\pm QvB}$
${\displaystyle F_{EB}=Q(E\pm vB)}$

## Electromagnetism

### Electromagnet

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

### Electromagnetic induction

Electromagnetic induction takes place in a circular loop and a coil of N circular loops . According to Faraday, change in magnetic field will produce electric potential

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

${\displaystyle B=Li={\frac {N\mu }{l}}i}$
${\displaystyle H={\frac {B}{\mu }}=i{\frac {N}{l}}}$

Maxwell's equation
${\displaystyle \nabla \cdot D=\rho }$
${\displaystyle \nabla \times E=-\nabla B}$
${\displaystyle \nabla \cdot B=0}$
${\displaystyle \nabla \times H=J+\nabla B}$

### Electromagnetism of a straight line conductor

 ${\displaystyle V=IR}$${\displaystyle I={\frac {V}{R}}}$${\displaystyle R={\frac {V}{I}}}$${\displaystyle G={\frac {I}{V}}}$${\displaystyle B=Li={\frac {\mu }{2\pi r}}i}$${\displaystyle R(T)=R_{o}+nT}$${\displaystyle R(T)=R_{o}e^{nT}}$${\displaystyle E_{R}=i^{2}R(T)=mC\Delta T}$${\displaystyle E_{V}=iv}$${\displaystyle E=E_{V}-E_{R}}$${\displaystyle m={\frac {i^{2}R(T)}{C\Delta T}}}$${\displaystyle C={\frac {i^{2}R(T)}{m\Delta T}}}$

### Electromagnetism of a circular loop conductor

 ${\displaystyle B=Li={\frac {\mu }{2r}}i}$${\displaystyle V={\frac {dB}{dt}}=L{\frac {di}{dt}}}$${\displaystyle F_{r}=F_{B}}$${\displaystyle m{\frac {v^{2}}{r}}=QvB}$${\displaystyle v={\frac {Q}{m}}Br}$${\displaystyle r={\frac {mv}{QB}}}$

### Electromagnetism of a coil of N circular loops

 Electromagnet ${\displaystyle B=LI=\mu i{\frac {N}{l}}}$${\displaystyle L=\mu {\frac {N}{l}}}$ ${\displaystyle -\phi =-NB=-NLi=-{\frac {N^{2}\mu i}{l}}}$${\displaystyle H={\frac {B}{\mu }}=N\mu i}$ Electromagnetic induction ${\displaystyle V={\frac {dB}{dt}}=L{\frac {di}{dt}}}$${\displaystyle \epsilon =-{\frac {d\phi }{dt}}=-NL{\frac {di}{dt}}}$ Electromagnetic oscillation ${\displaystyle \nabla \cdot E=0}$ ${\displaystyle \nabla \times E=-{\frac {1}{T}}E}$ ${\displaystyle \nabla \cdot B=0}$ ${\displaystyle \nabla \times B=-{\frac {1}{T}}B}$ ${\displaystyle T=\mu \epsilon }$ Electromagnetic wave Electromagnetic wave equation ${\displaystyle \nabla ^{2}E=-\omega E}$ ${\displaystyle \nabla ^{2}B=-\omega B}$ Electromagnetic wave function ${\displaystyle E=A\sin \omega t}$ ${\displaystyle B=A\sin \omega t}$ ${\displaystyle \omega =\lambda f={\sqrt {\frac {1}{T}}}=C}$ ${\displaystyle T=\mu \epsilon }$ ≈≈≈ Electromagnetic wave radiation ${\displaystyle v=\omega =\lambda f={\sqrt {\frac {1}{\mu \epsilon }}}=C}$ ${\displaystyle E=pv=pC=p\lambda f=hf=h{\frac {\omega }{2\pi }}=\hbar \omega }$ ${\displaystyle h=p\lambda =h{\frac {k}{2\pi }}=\hbar k}$ ${\displaystyle p={\frac {h}{\lambda }}}$ ${\displaystyle \lambda ={\frac {h}{p}}={\frac {C}{f}}}$

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