Question about tensor form of Maxwell equation [closed]

By variating the Maxwell Lagrangian we get the equation of motion. The remaining two Maxwell equations can be written as $$\epsilon_{\mu\nu\rho\sigma}\partial^{\rho} F^{\mu\nu} = 0.$$ I have also seen it written as the Bianchi identity: $$\partial_{[\lambda}F_{\mu\nu]} = 0.$$ Why are these two forms equivalent?

closed as off-topic by user108787, user36790, ACuriousMind♦, Jon Custer, GertSep 21 '16 at 2:15

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "Homework-like questions should ask about a specific physics concept and show some effort to work through the problem. We want our questions to be useful to the broader community, and to future users. See our meta site for more guidance on how to edit your question to make it better" – Community, Community, ACuriousMind, Jon Custer, Gert
If this question can be reworded to fit the rules in the help center, please edit the question.

• Please see edit. It's important to use understandable punctuation etc. so that others can understand the question. – DanielSank Sep 17 '16 at 14:06
• Have you tried plugging in the components of $F_{\mu \nu}$? Both forms are equivalent to the same two Maxwell equations, thus they are obviously mutually equivalent. – Prof. Legolasov Sep 17 '16 at 14:35
• VTC due to insufficient research, sorry. – user108787 Sep 17 '16 at 15:11
• I know they are equivalent by plugging the components of $F_{\mu\nu}$, But can we prove it by pure mathematicas only with $F_{\mu\nu}$ is antisymmetric. – Xian-Hui Sep 18 '16 at 10:20
• In both expressions everything is explicitly antisymmetrized, so I think you don't need antisymmetry of F. – Simon Sep 18 '16 at 23:59

Going from the second equation to the first is easy, just hit it with $\epsilon_{\mu\nu\rho\sigma}$.
Going from the first to the second equation, is a little trickier and relies on knowing how to evaluate the products of Levi-Civita symbols. The basic idea is that you should contact the first equation with $\epsilon^{\mu'\nu'\lambda'\sigma}$ and compare the resulting antisymmetric combination of $\delta$s with the antisymmetrization of the indices in the second equation.