3
votes
2answers
130 views

Classical Viewpoint on Electromagnetism

Note: This question may be difficult or impossible to answer within the rules of these forums due to its philosophical nature. I will delete the question if I am violating the rules. Onto the ...
2
votes
4answers
224 views

Why ONLY Maxwell's equations are the basic equations of electromagnetism?

In electromagnetism we say that all the electromagnetic interactions are governed by the 4 golden rules of Maxwell. But I want to know: is this(to assume that there is no requirement of any other ...
6
votes
1answer
310 views

Recovering all of Maxwell's equations from the variational principle

Whether you can get the first couple of Maxwell equations from a variational principle? In the second volume of the Landau theoretical physics said that it is impossible.
3
votes
2answers
124 views

When to use which representation for an electric field

In class we covered three types of possibilities to evaluate the electric field for static problems. Unfortunately, most physics textbooks cover these ways without addressing the question of ...
1
vote
3answers
182 views

Integration constants in Maxwell's equations (ambiguousness?)

In classical electrodynamics, if the electric field (or magnetic field, either of the two) is fully known (for simplicity: in a vacuum with $\rho = 0, \vec{j} = 0$), is it possible to unambiguously ...
4
votes
2answers
300 views

When studying electrodynamics do we assume Maxwell's Equations or derive them?

This question is because something made me confused. I always thought that the idea behind electrodynamics was to postulate some things, like Coulomb's law in electrostatics and so on, and then ...
-1
votes
1answer
172 views

Gauss's / Divergence theorem in Classical electrodynamics for the Electric field [duplicate]

Can somebody explain the proof of Gauss's theorem / divergence theorem taking the vector as electric field $$\iiint(\nabla\cdot\vec E)\mbox{ d} V=\iint \vec E \cdot\hat{n} \mbox{ d} ...
2
votes
1answer
185 views

Why is there no (time derivative of charge density) in the $B$ field in Jefimenko's equations?

I was going through Griffiths chapter on potentials and fields just to brush up on a few old things. He gets to Jefimenko's equations by this general path: Maxwell's equations Introduce scalar and ...
6
votes
3answers
1k views

Maxwells Equation from Electromagnetic Lagrangian

In Heaviside-Lorentz units the Maxwell's equations are: $$\nabla \cdot \vec{E} = \rho $$ $$ \nabla \times \vec{B} - \frac{\partial \vec{E}}{\partial t} = \vec{J}$$ $$ \nabla \times \vec{E} + ...
3
votes
2answers
202 views

Magnetostatics of Current-Carrying wire

A question has been nagging at me about Faraday's Law as related to a wire with a constant current: If you have a circular loop of wire with some small resistivity, connected to a battery so that it ...
36
votes
8answers
3k views

Do Maxwell's Equations overdetermine the electric and magnetic fields?

Maxwell's equations specify two vector and two scalar (differential) equations. That implies 8 components in the equations. But between vector fields $\vec{E}=(E_x,E_y,E_z)$ and ...