Recent content by Bob44

I set up an electrodynamics experiment with an axial symmetry which causes the vector potential to vanish. The Lorenz gauge $$\nabla \cdot \mathbf{A} = - \frac{1}{c^2} \frac{\partial \phi}{\partial t}$$ is usually employed in electrodynamic situations so that the scalar and vector potentials...

Imagine that two charged particles, with charge ##+q##, start at the origin and then move apart symmetrically on the ##+y## and ##-y## axes due to their electrostatic repulsion. The ##y##-component of the retarded Liénard-Wiechert vector potential at a point along the ##x##-axis due to the two...

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? $$\nabla \cdot (-\nabla \phi-\frac{\partial \mathbf{A}}{\partial t})=\frac{\rho}{\epsilon_0}$$ If ##\partial_t \mathbf{A}=0## due to constant current then we just have Poisson’s equation which has instantaneous...

Maxwell’s equations imply the following wave equation for the electric field $$\nabla^2\mathbf{E}-\frac{1}{c^2}\frac{\partial^2\mathbf{E}}{\partial t^2} = \frac{1}{\varepsilon_0}\nabla\rho+\mu_0\frac{\partial\mathbf J}{\partial t}.\tag{1}$$ I wonder if eqn.##(1)## can be split into the following...

This argument is another version of my previous post. Imagine that we have two long vertical wires connected either side of a charged sphere. We connect the two wires to the charged sphere simultaneously so that it is discharged by equal and opposite currents. Using the Lorenz gauge...

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.

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 charged sphere. By Gauss’ law the total electric flux through the Gaussian surface is equal to the total charge inside divided by ##\epsilon_0##. By symmetry...

Hi, I'm a Physics graduate who is still interested in the big questions of physics! Bob

Imagine a charged sphere at the origin connected through an open switch to a vertical grounded wire. We wish to find an expression for the horizontal component of the electric field at a distance ##\mathbf{r}## from the sphere as it discharges. By using the Lorenz gauge condition: $$\nabla...