Does a Magnetic Field Emerge from a Moving Charge with Constant Angular Speed?

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Discussion Overview

The discussion revolves around whether a magnetic field emerges from a moving charge with constant angular speed. Participants explore the implications of circular motion of charges and the associated electromagnetic fields, touching on theoretical and mathematical aspects.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants question the existence of a magnetic field if a charge is moving in a circular path, suggesting that centripetal acceleration implies some force must be acting on the charge.
  • One participant proposes that a charged pith ball on a rotating disk could serve as a practical example of a charge in circular motion.
  • There is a suggestion to solve for the potential field and coordinates of the particle, although uncertainty remains about the methodology.
  • Another participant mentions that a solution might overlook the fields generated by an accelerating charge, proposing a specific form for the magnetic field in spherical coordinates.
  • One participant references classical electrodynamics textbooks for further exploration of the electromagnetic fields due to moving charges, specifically mentioning synchrotron radiation.
  • A later reply expresses self-doubt about the validity of the initial question, indicating a perceived lack of clarity or relevance.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between circular motion and the emergence of magnetic fields, with no consensus reached on the initial question or the implications of the discussed scenarios.

Contextual Notes

Some participants note that the discussion may depend on specific assumptions about the motion of the charge and the definitions of the fields involved. There are unresolved mathematical steps regarding the derivation of the fields generated by the moving charge.

Timothy S
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If I write the lagrangian for a moving charge with constant angular speed, would a magnetic field be emergent? I would do the math myself, but I'm nowhere near pen and paper.
 
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Timothy S said:
If I write the lagrangian for a moving charge with constant angular speed, would a magnetic field be emergent? I would do the math myself, but I'm nowhere near pen and paper.
First of all, if there is no magnetic field to begin with why would a charge spin in circles? Spinning in circles implies there is some kind of force, because there is a centripetal acceleration, without centripetal acceleration there is no circular motion.
 
Alexandre said:
First of all, if there is no magnetic field to begin with why would a charge spin in circles? Spinning in circles implies there is some kind of force, because there is a centripetal acceleration, without centripetal acceleration there is no circular motion.

A charged pith ball on the edge of a rotating disk, driven at constant angular velocity, would suffice.
 
stedwards said:
A charged pith ball on the edge of a rotating disk, driven at constant angular velocity, would suffice.
I think you need to solve for potential field and coordinate of the particle. But I'm not sure how, check this out
https://people.ifm.liu.se/irina/teaching/sem4.pdf
 
Alexandre said:
I think you need to solve for potential field and coordinate of the particle. But I'm not sure how, check this out
https://people.ifm.liu.se/irina/teaching/sem4.pdf

For whatever reason, that solution seems to leave out the fields generated by the accelerating charge, though I only scanned the paper. There should be a magnetic field in the far field having an intensity something like ##B_z(r,\theta) = (1/r^2 sin \theta) cos(\omega t +f(\rho,t))##, in standard spherical coordinates, accompanied by a perpendicular electric field.
 
I'm not sure, what the question is about. If you have given the motion of a charge, maybe you want to know the electromagnetic field due to this moving charge. You find this problem for circular motion in almost any textbook on classical electrodynamics. Look for synchrotron radiation. A good treatment can be found in Landau/Lifshitz vol. II and, of course, Jackson, Classical Electrodynamics.
 
Sorry it was a really stupid question on so many levels.
 

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