Fundamental problem in electrostatics

[Kolahal Bhattacharya]

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?

 

[FrogPad]

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.

 

[Kolahal Bhattacharya]

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.

 

[StatMechGuy]

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".

 

[Kolahal Bhattacharya]

Yes!Of course.