Title: ETH_Sem4 / ED / Woche_04

Q: Definition Lorentz Kraft:
 [...]
A: \(F = e( E + \frac v c \wedge B)\)

Q: Magnetisches Dipol: \(\vec m\)
[...]\(= \) [...]
A: \(\vec A\); \(rot \frac{\vec m}{4\pi r}\)

Q: Homogene Feldgleichungen:
[...]
[...]
A: \(div B = 0\); \(rot E + \frac 1 c \dede{B}{t} = 0\)

Q: Inhomogene Feldgleichungen:
[...]
[...]
A: \(rotB - \frac 1 c \dede{E}{t} = \frac{i}{c}\); \(div E = \rho\)

Q: Kontinuitätsgleichung:
[...]
A: \(div(i) + \dede{\rho}{t} = 0\)

Q: Lorentz Kraftdichte:
[...]
A: \(f = \rho E + \frac i c \wedge B\)

Q: Identität:
 [...] \(=\) [...]
A: \(rot (rot( E)) \); \(\vec \nabla div(E) - \Delta E\)

Q: D'Allembert opperator:
[...]
A: \(\square = \frac 1 {c^2} \partial^2_t - \Delta\)

Q: Energiedichte des Feldes:
[...]
A: \(u := \frac 1 2 ( E^2 + B^2)\)

Q: Energiestromdichte des Feldes (Poynting Vektor)
[...]
A: \(\vec S := c(E \wedge B)\)

Q: Felder durch Potentiale:
[...]
[...]
A: \(B = rot A\); \(E = -\nabla \varphi- \frac 1 c \dede{A}{t}\)

Q: Inhomogene MGl mit Potentialen:
[...]
[...]
A: \(\square \varphi - \frac 1 c \dede{}{t}(\frac 1 c \dede \varphi t + div A) = \rho\); \(\square A + \nabla (\frac 1 c \dede{\varphi}{t} + div A ) = \frac i c\)

Q: Eichtransformationen des Feldes:
[...]
[...]
A: \(\varphi \to \varphi - \frac 1 c \dede{\chi}{t}\); \(A \to A + \nabla \chi\)

Eichungen:
- Lorenz-Eichung
  - \(\frac 1 c \dede{\varphi}{t} + div A =0 \)
- Coulomb Eichung
  - \(divA = 0\)

Q: Verbleibende Eichtransformationen nach Eichung:
Lorenz:
[...]
Coulomb:
[...]
A: \(\square \chi = 0\); \(\Delta \chi = 0\)

Q: Inhomogene MGl [...] Eichung:
[...]
[...]
A: Lorenz; \(\square \varphi = \rho\); \(\square A = \frac i c\)

Q: Inhomogene MGl [...] Eichung:
[...]
[...]
A: Coulomb; \(\Delta \varphi = -\rho\); \(\square A + \nabla(\frac 1 c \dede{\varphi}{t}) = \frac i c\)

Q: Freies Feld: Coulomb Eichung
[...]
[...]
A: \(\varphi = 0\); \(\square A = 0\)

Q: Polarisation Basen:
[...]
[...]
A: \(\varepsilon_{1,2} = e_{1,2}\) (linear); \(\varepsilon_{\pm} = \frac{1}{\sqrt{2} }(e_1 \pm i e_2)\) (zirkular)