Tensor notation of Maxwell's equation read
$$\partial_\mu F^{\mu\nu} = j^\nu.$$
So when we explicitly try to find the Maxwell's equation from the above tensor equation we only get gauss law and curl of B. The div.B=0 and curl of E are not present. What is happening here??
I have obtained the above tensor equation from the four maxwell equation but when i try explicitly write the equation component wise some how two of those equations dont appear?
I know it has something to do with two of those equations not being equations of motion, but i m still very unclear about this.
Best Answer
As is written here the two remaining equations follow from the Bianchi identity which says that the anti-symmetrized derivative is zero, ie. $$ \partial_{[a} F_{bc]} = \partial_{a} F_{bc}+\partial_{b} F_{ca}+\partial_{c} F_{ab} = 0 $$ (remember the $F_{\mu\nu}$ is antisymmetric itself!)