Maxwell stress tensor: Difference between revisions

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In physics, the Maxwell stress tensor is the stress tensor of an electromagnetic field. It is given by

\sigma _{\alpha \beta }={\frac {1}{4\pi }}E_{\alpha }E_{\beta }+H_{\alpha }H_{\beta }-{\frac {1}{2}}(E^{2}+H^{2})\delta _{\alpha \beta }

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 In [[physics]], the '''Maxwell stress tensor''' is the [[stress tensor]] of an [[electromagnetic field]]. It is given by
-:<math>T^{\alpha\beta} = \frac{1}{4\pi} [ -F^{\alpha \gamma}F_{\gamma}^{\beta}+\frac{1}{4}g^{\alpha\beta}F_{\gamma\delta}F^{\gamma\delta}]</math>.
+:<math>\sigma_{\alpha\beta}=\frac{1}{4\pi}E_{\alpha}E_{\beta}+H_{\alpha}H_{\beta}-
-And in explicit matrix form:
-:<math>T^{\alpha\beta} =\begin{bmatrix} \frac{E^2+B^2}{8\pi} & \frac{S_x}{c} & \frac{S_y}{c} & \frac{S_z}{c} \\ \frac{S_x}{c} & -\sigma_{xx} & -\sigma_{xy} & -\sigma_{xz} \\
-\frac{S_y}{c} & -\sigma_{yx} & -\sigma_{yy} & -\sigma_{yz} \\
-\frac{S_z}{c} & -\sigma_{zx} & -\sigma_{zy} & -\sigma_{zz} \end{bmatrix}</math>
-where
-:<math>\overrightarrow{S}=\frac{c}{4\pi}\overrightarrow{E}\times\overrightarrow{H}</math> is [[Poynting vector]],
-:<math>F_{\alpha\beta}</math> is the [[Electromagnetic field tensor]],
-:<math>g_{\alpha\beta}</math> is the metric tensor and
-:<math>\sigma_{\alpha\beta}</math> is defined by <math>\sigma_{\alpha\beta}=\frac{1}{4\pi}E_{\alpha}E_{\beta}+H_{\alpha}H_{\beta}-
 \frac{1}{2}(E^2+H^2)\delta_{\alpha\beta}</math>
 ==See also==
 *[[electromagnetic energy density]]
+*[[Energy momentum tensor]]
 [[Category:Tensors]]