Light Reflection and Feynmans plane of oscillating charges

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SUMMARY

In chapter 30-7 of Richard Feynman's Lectures on Physics, the relationship between the electric field of a plane of oscillating charges and the velocity of those charges is established, indicating that the field is in phase with the negative velocity at any distance. This leads to confusion regarding light reflection, as the phase shift of the electric field appears to be 90°, rather than the expected 180° necessary to cancel an incoming electromagnetic wave. The discussion highlights a potential misunderstanding in the application of Feynman's principles, particularly in relation to the phase shifts involved in charge acceleration and light interaction.

PREREQUISITES
  • Understanding of electromagnetic waves and their properties
  • Familiarity with Feynman's Lectures on Physics, specifically chapters 30 and 33
  • Knowledge of oscillating charges and their electric fields
  • Basic concepts of phase shifts in wave mechanics
NEXT STEPS
  • Review Feynman's Lectures on Physics, focusing on the derivation of electric fields from oscillating charges
  • Study the principles of electromagnetic wave reflection and phase shifts
  • Explore the mathematical formulation of retarded time in electromagnetic theory
  • Investigate the behavior of charges in conductive materials, particularly in relation to light interaction
USEFUL FOR

Students of physics, particularly those studying electromagnetism, educators teaching advanced physics concepts, and researchers exploring the interaction of light with charged particles.

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In ch 30-7 of the Lectures, Feynman explains that the field of a plane of oscillating charges at a point P is proportional to the velocity of the charges, considered at the appropriate retarded time (retarded by the vertical distance from the point P).
Feynman derives this formula only for large distance but says that it also works for any other distance.

This implies that directly at the plane of the charges, the electrical field is in phase with the (negative) velocity of the charges (and the same is true at a distance of one, two, three... wavelengths).

What is puzzling me is that this does not seem to allow for correct reflection of light.
If I have an incident em wave, this wave accelerates the charges. The acceleration is in phase with the wave (if the charges are sufficiently free as in a metal), so the vleocity of the charges is shifted by 90° in phase (when the acceleration is maximal, the velocity is zero - at the turning point of the oscillation). If the electrical field is in phase with the velocity, then the electrical field created by the plane of charges is phase-shifted by 90°, not by 180° as it should be to cancel the incoming wave.

Probably I'm making a stupid mistake somewhere, just cannot figure out where.
 
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Hi, I've only read this post now but I have exactly the same problem! Later in chapter 33 he says that it is possible to show by knowing the field for a layer of charge that the shift should be 180° but it seems just the opposite. Have you solved this problem?
 

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