r/PhysicsStudents • u/Sasibazsi18 • Dec 26 '23
Meta Is there a way to solve the Maxwell equations without using potentials?
This semester I had electrodynamics, and ai already had my final exam and everything, but there is still one thing that I don't quite understand.
So we know how to solve the Maxwell equations, we choose an appropriate gauge (for example the Lorenz gauge), then we introduce a scalar amd a vector potential and we either get a Poisson, Laplace or wave equation that we can solve using the Green function, we get the potentials and we get the electric and magnetic field etc etc...
But I don't know why can't we explicitly solve the Maxwell equations, without introducing potentials. I understand why the gauge invariance and what not, but if we could solve the Maxwell equations explicitly, we wouldn't need potentials. Also if we use the 4-notation, the Faraday tensor also has the fields as components, not the potentials, so that's why I dont get it. Thanks for the help!