# 3.2 Maxwell equations in four dimensions

A First Course in String Theory

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(a) Show explicitly that the source-free Maxwell equations emerge from $\displaystyle{T_{\mu \lambda \nu} = 0}$.

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\displaystyle{ \begin{aligned} T_{\mu \lambda \nu} &= 0 \\ \partial_\lambda F_{\mu \nu} + \partial_\mu F_{\nu \lambda} + \partial_\nu F_{\lambda \mu} &= 0 \\ \end{aligned}}

\displaystyle{ \begin{aligned} \partial_0 F_{1 3} + \partial_1 F_{3 0} + \partial_3 F_{0 1} &= 0 \\ - \partial_0 B_y + \partial_1 E_z - \partial_3 E_x &= 0 \\ \\ \frac{\partial E_x}{\partial z} - \frac{\partial E_z}{\partial x} &= - \frac{1}{c} \frac{\partial B_y}{\partial t} \\ \end{aligned}}

— Me@2022.09.11 01:40:50 PM

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