Fundamental problem in electrostatics

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  • Thread starter Thread starter Kolahal Bhattacharya
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    Electrostatics Fundamental
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Discussion Overview

The discussion revolves around the conditions under which a test charge can be considered to be moving very slowly in the context of electrostatics. Participants explore the implications of a moving charge on electric and magnetic fields, particularly when the charge moves at significant fractions of the speed of light.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants question the implications of a test charge moving at speeds that are a significant fraction of the speed of light, suggesting that this could complicate the analysis by introducing magnetic fields and time-varying electric fields.
  • One participant notes that moving a charge creates a current, which in turn generates a magnetic field, leading to additional complexities that are not accounted for in electrostatics.
  • Another participant emphasizes that even a single moving charge results in a non-steady current, which induces time-varying electric and magnetic fields, complicating the electrostatic framework.
  • It is proposed that using CGS or Gaussian units clarifies that magnetic effects are proportional to the velocity of the charge relative to the speed of light, indicating that these effects are negligible when the charge moves slowly.

Areas of Agreement / Disagreement

Participants express differing views on the significance of magnetic effects and time-varying fields in relation to the speed of the test charge. There is no consensus on the implications of these effects for electrostatics.

Contextual Notes

Participants acknowledge limitations in the analysis, particularly regarding the assumptions made about the speed of the charge and the resulting fields. The discussion highlights the dependence on definitions of "slow" and the potential for significant fluctuations in fields at higher speeds.

Who May Find This Useful

This discussion may be of interest to those studying electrostatics, electromagnetism, or related fields in physics, particularly in understanding the implications of charge motion on electric and magnetic fields.

Kolahal Bhattacharya
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Can someone say why it is said that in electrostatics,the test charge may be moving very slowly?Specifically,what is wrong if the test charge moves at a speed which is a significant proper fraction of speed of light?
 
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Kolahal Bhattacharya said:
Can someone say why it is said that in electrostatics,the test charge may be moving very slowly?Specifically,what is wrong if the test charge moves at a speed which is a significant proper fraction of speed of light?

From my little understanding... (warning: which could be wrong )
When you move a charge you create current, which creates a magnetic field, which creates an electric field. The calculation becomes messy. Plus, electrostatics doesn't worry itself with time-varying fields. Also moving a significant fraction of the speed of light then brings in relativistic effects.
 
I see.Let me concretize:
In electrostatics,we neglect magnetic effects and time varying effects.Now,a single moving charge,even running at a constant speed,results in a non-steady current,and that in turn,will result in a time-varying magnetic field.This,again,will induce a time varying electric field.
Now,if the speed is very small,we will have a slight fluctuation and if the speed is high,the magnitude of current,and hence,the resulting E and B fields will be big.So,electrostatics will make a mess with big fluctuations in fields and magnetic effects.
 
If people would use CGS or Gaussian units, it would be apparent that the magnetic effects are proportional to v/c, so it's a very small effect indeed. Thus, "slowly" basically means "a negligible fraction of the speed of light".
 
Yes!Of course.
 

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