Electromagnetics

Lorentz force

• almost all forces in mechanics are conservative forces, those that are functions nly of positions, and certainly not functions of velocities
• Lorentz force is a rare example of velocity dependent force

 

 

polarization of light

• has two possibilites
  
  • what does this mean?

 

Maxwell's equations

\(\nabla \cdot \mathbf{E} = \frac {\rho} {\varepsilon_0}\)

\(\nabla \cdot \mathbf{B} = 0\)

\(\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}\)

\(\nabla \times \mathbf{B} = \mu_0\mathbf{J} + \mu_0 \varepsilon_0 \frac{\partial \mathbf{E}} {\partial t}\ \)

 

 

Covariant formulation

\(F_{\alpha \beta} = \left( \begin{matrix} 0 & \frac{E_x}{c} & \frac{E_y}{c} & \frac{E_z}{c} \\ \frac{-E_x}{c} & 0 & -B_z & B_y \\ \frac{-E_y}{c} & B_z & 0 & -B_x \\ \frac{-E_z}{c} & -B_y & B_x & 0 \end{matrix} \right)\)

\(F_{\alpha \beta} = \partial_{\alpha} A_{\beta} - \partial_{\beta} A_{\alpha}\)

 

 

electromagnetic field

• an example of four-vector
• gague field describing the photon
• composed of a scalar electric potential and a three-vector magnetic potential

 

 

four-current

• charge density and current density
• http://en.wikipedia.org/wiki/Four-current

\[J^a = \left(c \rho, \mathbf{j} \right)\]

where

c is the speed of light

ρ the charge density

j the conventional current density.

a labels the space-time dimensions

 

four vector potential

• this is what we call the electromagnetic field

 

 

 

 

 

 

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참고할만한 자료

• http://ko.wikipedia.org/wiki/
• http://en.wikipedia.org/wiki/Classical_electromagnetism
• http://en.wikipedia.org/wiki/Maxwell's_equations
• http://en.wikipedia.org/wiki/Covariant_formulation_of_classical_electromagnetism
• http://en.wikipedia.org/wiki/electrical_current
• http://en.wikipedia.org/wiki/Four-current

• http://www.zentralblatt-math.org/zmath/en/
• http://pythagoras0.springnote.com/
• http://math.berkeley.edu/~reb/papers/index.html

• http://viswiki.com/en/
• http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q=
• http://www.ams.org/mathscinet/search/publications.html?pg4=AUCN&s4=&co4=AND&pg5=TI&s5=&co5=AND&pg6=PC&s6=&co6=AND&pg7=ALLF&co7=AND&Submit=Search&dr=all&yrop=eq&arg3=&yearRangeFirst=&yearRangeSecond=&pg8=ET&s8=All&s7=
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