Electric Field In Medium Clarification

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In a vacuum, the electric displacement field D is described by the equation D = ε0E + P, where P is the polarization that equals zero in vacuum. It is established that the electric field E in a vacuum is greater than in an insulating medium, assuming P does not oppose the electric field direction. However, in certain metamaterials, P can oppose the electric field, leading to different behavior for oscillating electromagnetic fields at specific frequencies. This clarification highlights the complexity of electric fields in various media. Understanding these nuances is crucial for applications in advanced materials and electromagnetic theory.
Danen
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So I just wanted to clarify:

Because D = ε0E + P

P being zero in vacuum
and ∇D is constant regardless of medium

if D was originally in a vacuum, the corresponding E would be greater than if it were in an insulating medium. So,

E in vacuum > E in medium
 
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Not if you use materials where P is opposed to the direction of the electric field. That can happen in metamaterials for oscillating electromagnetic fields of specific frequencies.
 
Thanks for clearing that up mfb.
 
It may be shown from the equations of electromagnetism, by James Clerk Maxwell in the 1860’s, that the speed of light in the vacuum of free space is related to electric permittivity (ϵ) and magnetic permeability (μ) by the equation: c=1/√( μ ϵ ) . This value is a constant for the vacuum of free space and is independent of the motion of the observer. It was this fact, in part, that led Albert Einstein to Special Relativity.
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