Charge moving with a constant linear velocity....

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Discussion Overview

The discussion revolves around whether a charge moving with a constant linear velocity produces a magnetic field. Participants explore concepts from electromagnetism, particularly in the context of Maxwell's equations and special relativity, while addressing implications of motion and reference frames.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • Some participants assert that a charge moving with constant linear velocity does not produce a magnetic field, while others argue that it does.
  • One participant suggests using Lorentz invariance to derive the electromagnetic field from a charge at rest, indicating that both electric and magnetic components arise from a Lorentz boost.
  • Questions are raised about the detection of magnetic fields in practical scenarios, such as near a Van De Graaff generator, and whether this implies absolute motion or the existence of aether.
  • Several participants emphasize that the electromagnetic field is invariant and frame-independent, with electric and magnetic components being dependent on the observer's frame of reference.
  • Some argue that the absence of a magnetic field around a charged particle would indicate absolute rest, while others counter that this view is illogical and inconsistent with the principles of relativity.
  • There are calls for experimental evidence to support claims about magnetic fields produced by moving charges, with references to straight wires carrying constant currents as examples.
  • Participants discuss the implications of Lorentz transformations on the electromagnetic field strength tensor and the logical consistency of various models.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether a charge moving with constant linear velocity produces a magnetic field. Multiple competing views are presented, with ongoing debate about the implications of motion and reference frames.

Contextual Notes

Some discussions highlight the need for experimental confirmation of theoretical models, and there are mentions of missing parameter descriptions in the proposed models. The conversation reflects a range of interpretations of electromagnetic theory and its application to moving charges.

  • #61
Maciej Orman said:
Yes, except this is only a theory and if such was true we would have a method of absolute speed measuring using excess charge body as a sensor...
No you would not. For the reason I've given twice, and vanhees71 and A.T. have given at least once each.
 
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  • #62
Ibix said:
According to the link in my previous post, Rowland had a 20cm diameter ring charged to 10-7C spinning at 50 revs/s. And was able to detect a magnetic field from it, which suggests epic experimental skills to me.
No, triboelectric charging method creates volume charge for which there is no method of measurement... Thus suggesting that the charge is much larger than estimated...
 
  • #63
Maciej Orman said:
No, triboelectric charging method creates volume charge for which there is no method of measurement... Thus suggesting that the charge is much larger than estimated...
Reference please.
 
  • #64
Ibix said:
Reference, please. Note that simply citing the Rowland disc is not sufficient, since the results are entirely explicable in terms of the linear speed of the charges (see p98-9 of https://books.google.co.uk/books?id=MbSUqqzFDocC&pg=PA98&lpg=PA98&dq=rowland+disc+experiment&source=bl&ots=0OzuvkesWW&sig=G_oqn3m8UNNQmnz97pz9_tQXVyQ&hl=en&sa=X&ved=0ahUKEwiI3dfXo_LVAhWGC8AKHbvyCWsQ6AEIDTAB#v=onepage&q=rowland disc experiment&f=false).
The point of Rowland's experiment (and other similar experiments in the late 19th century) was to proof that electric currents are due to moving charges ("electrons"). Nowadays that sounds trivial, because according to our present understanding all electric currents (and magnetizations) are due to elementary particles, but at this time the very nature of electric charges and currents was not that clear.

If I understand the excerpt from the textbook right, you have a charged ring of radius ##R##. The corresponding current density is
$$\vec{j}(\vec{x})=\rho \vec{v}=\frac{q}{2 \pi R} \delta(\varrho-R) \delta(z) \omega \varrho \vec{e}_{\varphi},$$
where ##(\varrho,\varphi,z)## are standard cylinder coordinates. The corresponding magnetic field can be calculated using the vector potential (in Coulomb gauge),
$$\vec{A}(\vec{x})=\frac{1}{c} \int_{\mathbb{R}^3} \mathrm{d}^3 \vec{x} \frac{\vec{j}(\vec{x}')}{4 \pi |\vec{x}-\vec{x}'|},$$
and finally the magnetic field as
$$\vec{B}=\vec{\nabla} \times \vec{A}.$$
The integral can be found in some good textbooks (like Jackson), leading to elliptic functions.
 
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