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.
 

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