Mar
23
asked Does a Static E-field Increase the Gauge Invariant Vector Potential Without Bound?
Feb
19
revised Momentum of stationary electron in a curl free vector potential
added 4 characters in body
Feb
19
revised Momentum of stationary electron in a curl free vector potential
Include Carron's gauge invariant Maxwell's Equations.
Feb
16
revised Momentum of stationary electron in a curl free vector potential
change bold to vector markup
Feb
15
revised Momentum of stationary electron in a curl free vector potential
Challenges to the notion that **A** is arbitrary due to arbitrary choice of gauge.
Feb
15
comment Momentum of stationary electron in a curl free vector potential
Let us continue this discussion in chat.
Feb
15
comment Momentum of stationary electron in a curl free vector potential
The notion that q$\vec{A}$ is arbitrary/nonphysical seems to be contradicted by the empirical validation of the existence of the Ahronov-Bohm Effect. Also there is, a time-domain Ahronov-Bohm Effect reported by Nikolova, N. K. et al in "Detection of the Time-dependent Electromagnetic Potential at 1.3 GHz" (20). Also consider Carron, N.J. "On the Fields of a Torus and the Observability of the Vector Potential" (7.13).
Feb
15
comment Momentum of stationary electron in a curl free vector potential
Let me take a whack at it: q$\vec{A}$ is a measure of the momentum that would be imparted to the electron if $\vec{J}$, hence its associated $\vec{A}$, went to zero. The way this momentum is imparted to the electron is by the potential formulation of Faraday's law: $\vec{E} = -\vec{\nabla}\phi - \frac{\partial \vec{A}}{\partial t}$ The time-changing $\vec{A}$ produces a radiating $\vec{E}$ field that contains energy which may, if it encounters the electron, impart energy, hence momentum, to the electron. The energy in the radiating $\vec{E}$ is reduced subsequent to this interaction.
Feb
14
revised Momentum of stationary electron in a curl free vector potential
added 16 characters in body
Feb
14
revised Momentum of stationary electron in a curl free vector potential
added 2 characters in body
Feb
14
revised Momentum of stationary electron in a curl free vector potential
added 2 characters in body
Feb
14
comment Momentum of stationary electron in a curl free vector potential
Timaeus, please read the first paragraph of the revised question -- which dramatically simplifies and clarifies the question in a way that should allow you to similarly dramatically simplify and clarify your answer. I'm leaning toward accepting your answer but I would like this question and answer to be simple and clear enough that it can be more relevant.
Feb
14
comment Momentum of stationary electron in a curl free vector potential
Please see the first paragraph of the revised wording of the question.
Feb
14
revised Momentum of stationary electron in a curl free vector potential
Try to call out the essential question from the conditions imposed to avoid bogus answers.
Feb
13
comment Momentum of stationary electron in a curl free vector potential
You said: "It sounds like you want an electron, a statically charged torus, and then to consider the two cases of the torus with and without a current." No. The only reason I introduced the static charge to the torus was to construct the desired end state: No electric or magnetic fields outside the torus's minor radius, except the electric field of an electron at rest in that space. The two conditions are then 1) with an A field (which is neither electric nor magnetic) in that space and 2) without an A field in that space. Please don't say the electron contributed to the A.
Feb
12
awarded  Promoter
Feb
12
revised Momentum of stationary electron in a curl free vector potential
Get rid of questionable use of "conserved momentum" and elaborate the question to clarify no transfer of the electron's mv to the A field has occurred.
Feb
11
revised Momentum of stationary electron in a curl free vector potential
Clarify the source of the **E** field.
Feb
10
revised Momentum of stationary electron in a curl free vector potential
Reword the question so as to exclude any storage of mechanical momentum in **J** (hence in **A**).
Feb
9
revised Momentum of stationary electron in a curl free vector potential
added 6 characters in body