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8.1 SI und cgs

SI (MKSA) Gauß'sche Einheiten (cgs)

$\displaystyle \nabla$ ^. $\displaystyle \vec{E}\,$ = $\displaystyle {\rho \over {\epsilon_0}}$ $\displaystyle \nabla$ ^. $\displaystyle \vec{E}\,$ = 4 $\displaystyle \pi$ $\displaystyle \rho$

$\displaystyle \vec{E}\,$ = $\displaystyle {1 \over {4 \pi \epsilon_0}}$ $\displaystyle \int_{V}^{}$ $\displaystyle {{\rho \vec{r}} \over {r^3}}$ dV $\displaystyle \vec{E}\,$ = $\displaystyle \int_{V}^{}$ $\displaystyle {{\rho \vec{r}} \over {r^3}}$ dV

$\displaystyle \nabla$ x $\displaystyle \vec{E}\,$ = - $\displaystyle {{\partial \vec{B}}\over {\partial t}}$ c $\displaystyle \nabla$ x $\displaystyle \vec{E}\,$ = - $\displaystyle {{\partial \vec{B}}\over {\partial t}}$

$\displaystyle \vec{E}\,$ = - $\displaystyle \nabla$ $\displaystyle \phi$ - $\displaystyle {{\partial \vec{A}}\over {\partial t}}$ $\displaystyle \vec{E}\,$ = - $\displaystyle \nabla$ $\displaystyle \phi$ - $\displaystyle {1 \over c}$ $\displaystyle {{\partial \vec{A}}\over {\partial t}}$

$\displaystyle \nabla$ x $\displaystyle \vec{B}\,$ = $\displaystyle \mu_{0}^{}$ $\displaystyle \left(\vphantom{j + \epsilon_0 {{\partial E}\over {\partial t}} }\right.$ j + $\displaystyle \epsilon_{0}^{}$ $\displaystyle {{\partial E}\over {\partial t}}$ $\displaystyle \left.\vphantom{j + \epsilon_0 {{\partial E}\over {\partial t}} }\right)$ $\displaystyle \nabla$ x $\displaystyle \vec{B}\,$ = 4 $\displaystyle \pi$ j + $\displaystyle {1 \over c}$ $\displaystyle {{\partial E}\over {\partial t}}$

$\displaystyle \vec{B}\,$ = $\displaystyle {\mu_0 \over {4 \pi}}$ $\displaystyle \int$ $\displaystyle {{\left( j + \epsilon_0 {{\partial E}\over {\partial t}}\right) \times \vec{r}}\over {r^3}}$ dV $\displaystyle \vec{B}\,$ = $\displaystyle \int$ $\displaystyle {{\left( j + {1 \over {4 \pi c}} {{\partial E}\over {\partial t}}\right) \times \vec{r}}\over {r^3}}$ dV

$\displaystyle \nabla$ ^. $\displaystyle \vec{B}\,$ = 0 $\displaystyle \nabla$ ^. $\displaystyle \vec{B}\,$ = 0

$\displaystyle \vec{B}\,$ = $\displaystyle \nabla$ x $\displaystyle \vec{A}\,$ $\displaystyle \vec{B}\,$ = $\displaystyle \nabla$ x $\displaystyle \vec{A}\,$

$\displaystyle \nabla$ ^. $\displaystyle \vec{j}\,$ + $\displaystyle {{\partial \rho}\over {\partial t}}$ = 0 $\displaystyle \nabla$ ^. $\displaystyle \vec{j}\,$ + $\displaystyle {1 \over c}$ $\displaystyle {{\partial \rho}\over {\partial t}}$ = 0

$\displaystyle \nabla$ ^. $\displaystyle \vec{A}\,$ + $\displaystyle {1 \over c^2}$ $\displaystyle {{\partial \phi}\over {\partial t}}$ = 0 $\displaystyle \nabla$ ^. $\displaystyle \vec{A}\,$ + $\displaystyle {1 \over c}$ $\displaystyle {{\partial \phi}\over {\partial t}}$

$\displaystyle \vec{F}\,$ = e( $\displaystyle \vec{E}\,$ + $\displaystyle \vec{u}\,$ x $\displaystyle \vec{B}\,$ ) $\displaystyle \vec{F}\,$ = e( $\displaystyle \vec{E}\,$ + $\displaystyle {1 \over c}$ $\displaystyle \vec{u}\,$ x $\displaystyle \vec{B}\,$ )

$\displaystyle {{\partial F^{ij}}\over {\partial x^i}}$ = $\displaystyle {{j^j}\over {\epsilon_0}}$ $\displaystyle {{\partial F^{ij}}\over {\partial x^i}}$ = 4 $\displaystyle \pi$ j^j

wobei wobei

F^ij = $\left(\vphantom{ \begin{array}{cccc} 0 & -c B_z & c B_y & +E_x \\ c B_x & 0 &... ...\ -c b_y & c B_x & 0 & + E_z \\ -E_x & -E_y & -E_z & 0\\ \end{array}}\right.$ $\begin{array}{cccc} 0 & -c B_z & c B_y & +E_x \\ c B_x & 0 & -c B_z & +E_y \\ -c b_y & c B_x & 0 & + E_z \\ -E_x & -E_y & -E_z & 0\\ \end{array}$ $\left.\vphantom{ \begin{array}{cccc} 0 & -c B_z & c B_y & +E_x \\ c B_x & 0 &... ...\ -c b_y & c B_x & 0 & + E_z \\ -E_x & -E_y & -E_z & 0\\ \end{array}}\right)$ F^ij = $\left(\vphantom{ \begin{array}{cccc} 0 & - B_z & B_y & +E_x \\ B_x & 0 & -B_... ...y \\ - b_y & B_x & 0 & + E_z \\ -E_x & -E_y & -E_z & 0\\ \end{array}}\right.$ $\begin{array}{cccc} 0 & - B_z & B_y & +E_x \\ B_x & 0 & -B_z & +E_y \\ - b_y & B_x & 0 & + E_z \\ -E_x & -E_y & -E_z & 0\\ \end{array}$ $\left.\vphantom{ \begin{array}{cccc} 0 & - B_z & B_y & +E_x \\ B_x & 0 & -B_... ...y \\ - b_y & B_x & 0 & + E_z \\ -E_x & -E_y & -E_z & 0\\ \end{array}}\right)$

Alexander Wagner
2000-04-14

SI (MKSA)	Gauß'sche Einheiten (cgs)
$\displaystyle \nabla$ ^. $\displaystyle \vec{E}\,$ = $\displaystyle {\rho \over {\epsilon_0}}$	$\displaystyle \nabla$ ^. $\displaystyle \vec{E}\,$ = 4 $\displaystyle \pi$ $\displaystyle \rho$
$\displaystyle \vec{E}\,$ = $\displaystyle {1 \over {4 \pi \epsilon_0}}$ $\displaystyle \int_{V}^{}$ $\displaystyle {{\rho \vec{r}} \over {r^3}}$ dV	$\displaystyle \vec{E}\,$ = $\displaystyle \int_{V}^{}$ $\displaystyle {{\rho \vec{r}} \over {r^3}}$ dV
$\displaystyle \nabla$ `x` $\displaystyle \vec{E}\,$ = - $\displaystyle {{\partial \vec{B}}\over {\partial t}}$	c $\displaystyle \nabla$ `x` $\displaystyle \vec{E}\,$ = - $\displaystyle {{\partial \vec{B}}\over {\partial t}}$
$\displaystyle \vec{E}\,$ = - $\displaystyle \nabla$ $\displaystyle \phi$ - $\displaystyle {{\partial \vec{A}}\over {\partial t}}$	$\displaystyle \vec{E}\,$ = - $\displaystyle \nabla$ $\displaystyle \phi$ - $\displaystyle {1 \over c}$ $\displaystyle {{\partial \vec{A}}\over {\partial t}}$
$\displaystyle \nabla$ `x` $\displaystyle \vec{B}\,$ = $\displaystyle \mu_{0}^{}$ $\displaystyle \left(\vphantom{j + \epsilon_0 {{\partial E}\over {\partial t}} }\right.$ j + $\displaystyle \epsilon_{0}^{}$ $\displaystyle {{\partial E}\over {\partial t}}$ $\displaystyle \left.\vphantom{j + \epsilon_0 {{\partial E}\over {\partial t}} }\right)$	$\displaystyle \nabla$ `x` $\displaystyle \vec{B}\,$ = 4 $\displaystyle \pi$ j + $\displaystyle {1 \over c}$ $\displaystyle {{\partial E}\over {\partial t}}$
$\displaystyle \vec{B}\,$ = $\displaystyle {\mu_0 \over {4 \pi}}$ $\displaystyle \int$ $\displaystyle {{\left( j + \epsilon_0 {{\partial E}\over {\partial t}}\right) \times \vec{r}}\over {r^3}}$ dV	$\displaystyle \vec{B}\,$ = $\displaystyle \int$ $\displaystyle {{\left( j + {1 \over {4 \pi c}} {{\partial E}\over {\partial t}}\right) \times \vec{r}}\over {r^3}}$ dV
$\displaystyle \nabla$ ^. $\displaystyle \vec{B}\,$ = 0	$\displaystyle \nabla$ ^. $\displaystyle \vec{B}\,$ = 0
$\displaystyle \vec{B}\,$ = $\displaystyle \nabla$ `x` $\displaystyle \vec{A}\,$	$\displaystyle \vec{B}\,$ = $\displaystyle \nabla$ `x` $\displaystyle \vec{A}\,$
$\displaystyle \nabla$ ^. $\displaystyle \vec{j}\,$ + $\displaystyle {{\partial \rho}\over {\partial t}}$ = 0	$\displaystyle \nabla$ ^. $\displaystyle \vec{j}\,$ + $\displaystyle {1 \over c}$ $\displaystyle {{\partial \rho}\over {\partial t}}$ = 0
$\displaystyle \nabla$ ^. $\displaystyle \vec{A}\,$ + $\displaystyle {1 \over c^2}$ $\displaystyle {{\partial \phi}\over {\partial t}}$ = 0	$\displaystyle \nabla$ ^. $\displaystyle \vec{A}\,$ + $\displaystyle {1 \over c}$ $\displaystyle {{\partial \phi}\over {\partial t}}$
$\displaystyle \vec{F}\,$ = e( $\displaystyle \vec{E}\,$ + $\displaystyle \vec{u}\,$ `x` $\displaystyle \vec{B}\,$ )	$\displaystyle \vec{F}\,$ = e( $\displaystyle \vec{E}\,$ + $\displaystyle {1 \over c}$ $\displaystyle \vec{u}\,$ `x` $\displaystyle \vec{B}\,$ )
$\displaystyle {{\partial F^{ij}}\over {\partial x^i}}$ = $\displaystyle {{j^j}\over {\epsilon_0}}$	$\displaystyle {{\partial F^{ij}}\over {\partial x^i}}$ = 4 $\displaystyle \pi$ j^j
wobei	wobei
F^ij = $\left(\vphantom{ \begin{array}{cccc} 0 & -c B_z & c B_y & +E_x \\ c B_x & 0 &... ...\ -c b_y & c B_x & 0 & + E_z \\ -E_x & -E_y & -E_z & 0\\ \end{array}}\right.$ $\begin{array}{cccc} 0 & -c B_z & c B_y & +E_x \\ c B_x & 0 & -c B_z & +E_y \\ -c b_y & c B_x & 0 & + E_z \\ -E_x & -E_y & -E_z & 0\\ \end{array}$ $\left.\vphantom{ \begin{array}{cccc} 0 & -c B_z & c B_y & +E_x \\ c B_x & 0 &... ...\ -c b_y & c B_x & 0 & + E_z \\ -E_x & -E_y & -E_z & 0\\ \end{array}}\right)$	F^ij = $\left(\vphantom{ \begin{array}{cccc} 0 & - B_z & B_y & +E_x \\ B_x & 0 & -B_... ...y \\ - b_y & B_x & 0 & + E_z \\ -E_x & -E_y & -E_z & 0\\ \end{array}}\right.$ $\begin{array}{cccc} 0 & - B_z & B_y & +E_x \\ B_x & 0 & -B_z & +E_y \\ - b_y & B_x & 0 & + E_z \\ -E_x & -E_y & -E_z & 0\\ \end{array}$ $\left.\vphantom{ \begin{array}{cccc} 0 & - B_z & B_y & +E_x \\ B_x & 0 & -B_... ...y \\ - b_y & B_x & 0 & + E_z \\ -E_x & -E_y & -E_z & 0\\ \end{array}}\right)$