# 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
$F_{Q}=K{\frac {Q_{+}Q_{-}}{r^{2}}}$ 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
$F_{Q}=QE$ 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
$F_{B}=\pm QvB$ The sum of 2 forces Electromotive force and Electromagnetomotive force creates Electromagnetic force
$F_{EB}=F_{E}+F_{B}=QE\pm QvB=Q(E\pm vB)$ Electrostatic field

The force of attraction of 2 different charges

$F=K{\frac {Q_{-}Q_{+}}{r^{2}}}=K{\frac {Q^{2}}{r^{2}}}$ . $Q_{-}=Q+$ The electric field of the charge in motion

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

The potential of the electric field

$V=\int Edr={\frac {Q}{r}}$ ## Magnetostatics

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

### Electromagnet

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

$V={\frac {dB}{dt}}$ $\epsilon =-{\frac {d\phi }{dt}}$ 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

$B=Li={\frac {N\mu }{l}}i$ $H={\frac {B}{\mu }}=i{\frac {N}{l}}$ Maxwell's equation
$\nabla \cdot D=\rho$ $\nabla \times E=-\nabla B$ $\nabla \cdot B=0$ $\nabla \times H=J+\nabla B$ ### Electromagnetism of a straight line conductor $V=IR$ $I={\frac {V}{R}}$ $R={\frac {V}{I}}$ $G={\frac {I}{V}}$ $B=Li={\frac {\mu }{2\pi r}}i$ $R(T)=R_{o}+nT$ $R(T)=R_{o}e^{nT}$ $E_{R}=i^{2}R(T)=mC\Delta T$ $E_{V}=iv$ $E=E_{V}-E_{R}$ $m={\frac {i^{2}R(T)}{C\Delta T}}$ $C={\frac {i^{2}R(T)}{m\Delta T}}$ ### Electromagnetism of a circular loop conductor $B=Li={\frac {\mu }{2r}}i$ $V={\frac {dB}{dt}}=L{\frac {di}{dt}}$ $F_{r}=F_{B}$ $m{\frac {v^{2}}{r}}=QvB$ $v={\frac {Q}{m}}Br$ $r={\frac {mv}{QB}}$ ### Electromagnetism of a coil of N circular loops Electromagnet $B=LI=\mu i{\frac {N}{l}}$ $L=\mu {\frac {N}{l}}$ $-\phi =-NB=-NLi=-{\frac {N^{2}\mu i}{l}}$ $H={\frac {B}{\mu }}=N\mu i$ Electromagnetic induction $V={\frac {dB}{dt}}=L{\frac {di}{dt}}$ $\epsilon =-{\frac {d\phi }{dt}}=-NL{\frac {di}{dt}}$ Electromagnetic oscillation $\nabla \cdot E=0$ $\nabla \times E=-{\frac {1}{T}}E$ $\nabla \cdot B=0$ $\nabla \times B=-{\frac {1}{T}}B$ $T=\mu \epsilon$  Electromagnetic wave Electromagnetic wave equation $\nabla ^{2}E=-\omega E$ $\nabla ^{2}B=-\omega B$ Electromagnetic wave function $E=A\sin \omega t$ $B=A\sin \omega t$ $\omega =\lambda f={\sqrt {\frac {1}{T}}}=C$ $T=\mu \epsilon$ ≈≈≈ Electromagnetic wave radiation $v=\omega =\lambda f={\sqrt {\frac {1}{\mu \epsilon }}}=C$ $E=pv=pC=p\lambda f=hf=h{\frac {\omega }{2\pi }}=\hbar \omega$ $h=p\lambda =h{\frac {k}{2\pi }}=\hbar k$ $p={\frac {h}{\lambda }}$ $\lambda ={\frac {h}{p}}={\frac {C}{f}}$ 