Maxwell’s equations

Lets try to re-create maxwell equations

Guess 1

🐌 Guess: here we guess that the following solution is true and we will verify it later

$$ \boxed{\partial _\mu F^{\mu \nu}=\mu_0 j^\nu} $$

Verification

Relation with wave equation

Guess 2

Lets try to uncover the other 2 Maxwell equations using

$$ \boxed{\partial ^\mu F^ {\nu \lambda}+\partial ^{\lambda } F^{\mu \nu} + \partial ^{\nu} F^{\lambda \mu}=0} $$

Verification

Interaction of charged particles with E and B fields

Lets try to get something analogous to $F=ma$ but for electromagnetism

Guess