Electrodynamics, Curl of P and D

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SUMMARY

The discussion centers on the relationship between the curl of electric displacement field (D) and polarization field (P) in electrostatics, specifically under the condition where the magnetic field (B) is static. It is established that in linear media, the curls of both D and P are zero, which simplifies the analysis of electric fields. The user seeks a deeper understanding of the origins of these curls and whether they can be expressed independently of each other. This inquiry highlights the need for clarity on the mathematical expressions governing these fields.

PREREQUISITES
  • Understanding of vector calculus, specifically curl and divergence operations.
  • Familiarity with Maxwell's equations and their implications in electrostatics.
  • Knowledge of linear dielectric materials and their properties.
  • Basic concepts of electromagnetic theory, particularly the relationship between electric and magnetic fields.
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  • Study the derivation of Maxwell's equations in electrostatics.
  • Explore the mathematical definitions and physical interpretations of curl and divergence in vector fields.
  • Investigate the properties of linear dielectric materials and their impact on electric fields.
  • Examine the relationship between electric displacement field (D) and polarization field (P) in various media.
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Students and professionals in physics, electrical engineering, and applied mathematics who are looking to deepen their understanding of electromagnetic theory and the behavior of electric fields in different media.

guiablo
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I know that in statics curl of P=curl of D, since the variation of B in time = 0, and I also know that for linear mediums those curls are 0, but I don't know why, and I don't know if there is any expresion always valid.

I would like to know where this curl comes from like I know where the curl and the divergence of magnetic/inducción/magnetitation field comes so I can picture the electric field in my head easier, as I do with magnetic field, thank you.
 
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I know this is valid always, but i would like to know if we can have the curl of D or P in an expresion that doesn't depend on the other one
 

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