Equationes De Maxwell

Equationes de Maxwell
	instantia de: Mathematical descriptions of the electromagnetic field[], physical theory[]
	subclasse de: partial differential equation[], physical law[]
	;
	Commons: Maxwell's equations

${\boldsymbol {\nabla .B}}=0$

${\boldsymbol {\nabla .E}}={\frac {\rho }{\epsilon _{0}}}$

${\boldsymbol {\nabla \times E}}=-{\frac {\delta {\boldsymbol {B}}}{\delta t}}$

${\boldsymbol {\nabla \times B}}=\epsilon _{0}{\boldsymbol {J}}+\epsilon _{0}\mu _{0}{\frac {\delta {\boldsymbol {E}}}{\delta t}}$

ubi E e B es le campo electric e le campo magnetic, unitates N/C e $tesla={\frac {V\cdot s}{m^{2}}}$ , respectivemente, essente un littera in nigretto un vector. De plus, $\rho$ es le densitate o quantitate de carga per unitate de volume, $\epsilon _{0}$ e $\mu _{0}$ son constantes fundamental appellate, respectivemente, le permissivitate e le permeabilitate del vacuo, o de plus appellate, constantes electric e magnetic del vacuo. Le vector J es le densitate de currente e t es le tempore. Le constantes electric e magnetic ha le valores

$\epsilon _{0}=8,854187817\cdot 10^{-12}{\frac {A\cdot s}{V\cdot m}}$

$\mu _{0}=12,566370614\cdot 10^{-7}{\frac {V\cdot s}{A\cdot m}}$

Le operator $\nabla$ ha character vectorial. Iste quatro equationes unifica le campo electric con le campo magnetic. Le leges de Maxwell involve taxas de variation con respecto al tempore e al coordinatas spatial. Iste ultime variationes spatial son appelate le gradiente, le divergentia e le rotational (symbol curl in anglese). Le mistura del campo electric E e magnetic B es solmente apparente, a causa del observation casual, essente que le un se transforma in le altere, dependente del stato de movimento relative del fonte del campo con relation al observator. Iste equationes pote esser scripte plus compactemente in notation tensorial, ubi illos se reduce a solmente duo equationes, del quales tote le theoria del lumine como un unda electromagnetic pote esser disveloppate.

Le prime lege de Maxwell stabiliva le non existentia del monopolo magnetic in le universo.

De su leges, Maxwell poteva demonstrar que le lumine consiste de un unda electromagnetic. Plus, que le duo campos vectorial, le campos electric E e le campo magnetic B, oscila perpendicularmente, un relative al altere. Pro monstrar isto, scripte le leges de Maxwell in le vacuo, ubi le densitates de carga e currente son nulle

${\boldsymbol {\nabla .B}}=0$

${\boldsymbol {\nabla .E}}=0$

${\boldsymbol {\nabla \times E}}=-{\frac {\delta {\boldsymbol {B}}}{\delta t}}$

${\boldsymbol {\nabla \times B}}=\epsilon _{0}\mu _{0}{\frac {\delta {\boldsymbol {E}}}{\delta t}}$

Nunc, opera con le operator nabla a sinistra de un del ultime equationes, appelate, equationes non-homogeneas, sia le ultime, per exemplo, pro obtener successivemente, usante alicun algebra vectorial

${\boldsymbol {\nabla \times }}({\boldsymbol {\nabla \times B}})=\epsilon _{0}\mu _{0}{\frac {\delta {\boldsymbol {\nabla \times E}}}{\delta t}}$

${\boldsymbol {\nabla }}({\boldsymbol {\nabla \times B}})-{\boldsymbol {\nabla }}^{2}{\boldsymbol {B}}=-\epsilon _{0}\mu _{0}{\frac {\delta ^{2}{\boldsymbol {B}}}{\delta t^{2}}}$

${\boldsymbol {\nabla }}^{2}{\boldsymbol {B}}=\epsilon _{0}\mu _{0}{\frac {\delta ^{2}{\boldsymbol {B}}}{\delta t^{2}}}$

Sed isto es un equation de unda pro le campo magnetic, essente le velocitate de iste unda equal a

$c={\frac {1}{(\epsilon _{0}\mu _{0})^{\frac {1}{2}}}}=299.792.458\ {\frac {m}{s}}$

o sia, le velocitate del lumine. Esque vos pote imaginar le placer de trovar um resultato como isto? Il es inimaginabile! Un equation similar pote esser disveloppate pro le equation de unda del campo electric per le mesmo methodo. Maxwell provava assi que le lumine es un unda electromagnetic.

(Plus tarde nos demonstra que le campos son perpendicular un al altere, ben como altere resultatos.)

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Equationes De Maxwell

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