Ambiguity of Curl in Maxwell-Faraday Equation

[greswd]

Again, a vector field is only completely specified when giving it's curl and its divergence together with the boundary conditions. Look for Helmholtz's fundamental theorem of vector calculus!

Do you need any clarifications with the notions in #23 and #27? (and I'm not trying to be rhetorically snarky)

 

[vanhees71]

As I said, I don't see the physics behind your artificial assumptions. You need to solve the complete set of Maxwell equations, not just one!

 

[Dale]

You need to solve the complete set of Maxwell equations, not just one!

I agree completely with this and all of my comments are assuming that we are looking for solutions to all of Maxwell's equations.

 

[rude man]

You don't need relativity or tensors to get a grip on this problem. You do need to use dynamic rather than static potentials; for example, the familiar E -= -∇V changes to E = -∇V - μ ∂A/∂t
where A is the vector potential such that H = ∇ x A = B/μ
and V is the scalar electric potential;
and Poisson's equation changes to ∇²V = -ρ/ε - μ ∂/∂t (∇⋅A) etc.
If you try to use static potentials you get that the E field around even a time-varying current is zero.
EDIT: I was assuming a long wire but what I said can be applied to your coil also.
The idea of retardation potentials is included in what I said FYI.