Deriving Maxwell's Eqs from Conservation Laws: E&M Fields

[Miviato]

Homework Statement

Can you derive Maxwell's equations from conservation of charge, energy and angular momentum for E&M fields?

Homework Equations

The Attempt at a Solution

 

[sunjin09]

Once you are able to define these quantities, including EM fields themselves, I'm sure you can. But without Maxwell's equations, how do you even define a charge?

 

[Mindscrape]

One could argue that the field theory approach, deriving Maxwell's equations from the Lagrangian with 4-vector potentials, is what you've asked about.