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The Helmholtz theorem states that any vector field can be uniquely decomposed into longitudinal (curl free) and transverse (divergence...

But the tangential magnetic field produced by the spark due to Stokes law is still instantaneous at all distances. This seems to...

Let us take the Ampere-Maxwell law $$\nabla \times \mathbf{B} = \mu_0\,\mathbf{J}+\frac{1}{c^2}\frac{\partial \mathbf{E}}{\partial...

Thanks for the reference! https://arxiv.org/abs/physics/0204034

This is shown in Jackson's 2002 paper "From Lorenz to Coulomb and other explicit gauge transformations" (Am J Phys, 35:832-837)...

But how could the retarded transverse field cancel the instantaneous longitudinal field as it takes a finite time for the transverse...

Scalar and vector potentials in Coulomb gauge Assume Coulomb gauge so that $$\nabla \cdot \mathbf{A}=0.\tag{1}$$ The scalar potential...

I set up an electrodynamics experiment with an axial symmetry which causes the vector potential to vanish. The Lorenz gauge $$\nabla...

Imagine that two charged particles, with charge ##+q##, start at the origin and then move apart symmetrically on the ##+y## and ##-y##...

I guess I should use ##\epsilon##, ##\mu## and ##c## appropriate to the material in the coaxial cable.

Is that also true if I derive Poisson’s equation from Gauss’s law and solve that? $$\nabla \cdot (-\nabla \phi-\frac{\partial...

Maxwell’s equations imply the following wave equation for the electric field...

Interesting. I guess as ##q(t)## is not arbitrary your example does not break causality as we cannot use it to signal faster than light.

The potential at the field point ##p## at time ##t## is given by the retarded-time expression ##\phi(r, t) = \large...

I’ve just used a spherical Gaussian surface with the same center as the charged sphere but with a larger radius so that it encloses the...