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Fundamental problem in electrostatics

  1. Feb 19, 2007 #1
    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?
  2. jcsd
  3. Feb 19, 2007 #2
    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.
  4. Feb 19, 2007 #3
    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.
  5. Feb 19, 2007 #4
    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".
  6. Feb 19, 2007 #5
    Yes!Of course.
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