Electric field of a point charge in uniform motion

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SUMMARY

The discussion focuses on the electric field of a point charge in uniform motion as described in Griffiths' "Introduction to Electrodynamics," specifically Chapter 12, page 527. Participants explore the implications of using polar coordinates, questioning the relevance of the z-coordinate and the dimensionality of the analysis. The consensus is that the electric field can be effectively analyzed in two dimensions while maintaining consistency with three-dimensional representations through appropriate coordinate transformations.

PREREQUISITES
  • Understanding of electric fields and point charges
  • Familiarity with Griffiths' "Introduction to Electrodynamics"
  • Knowledge of polar coordinates and their application in physics
  • Basic concepts of rotational symmetry in electromagnetism
NEXT STEPS
  • Study the derivation of electric fields for moving charges in Griffiths' text
  • Learn about the application of polar coordinates in three-dimensional physics
  • Research the implications of rotational symmetry in electromagnetic theory
  • Explore advanced topics in electrodynamics, such as the Liénard-Wiechert potentials
USEFUL FOR

This discussion is beneficial for physics students, educators, and researchers focusing on electromagnetism, particularly those studying the behavior of electric fields in relation to moving charges.

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In Griffiths Chapter 12, pg 527:

Suppose a point charge is moving along x, we obtain the following E-fields:

Questions

1. Is the vector R solely in the x-y plane?

2. What happened to the coordinate 'z' ?

3. Why are they only doing things in the 2-D plane? Can we use rotational symmetry somewhere?

2ih5bn4.png
 
Last edited:
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When instead, I assume the particle to be moving along z-axis it fixes everything!

and i use x=Rsinθcosø, y = Rsinθsinø, z = R cos ø

The end result turns out beautifully to be the one as described, in 3 dimensions:

2n9icmg.png



I suspect that since Polar coordinates is usually defined with θ as angle between R and z-axis and ø as angle in x-y plane, everything matches.
 
bumpp
 

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