Problem with understanding polarization

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SUMMARY

The discussion centers on the behavior of linear dielectrics under polarization, specifically addressing the contradiction arising from the equations \(\vec{E}=\frac{-1}{3\epsilon_{0}}\vec{P}\) and \(\vec{P}=(\epsilon - \epsilon_{0})\vec{E}\). It is established that if a linear dielectric is polarized without an external electric field, it cannot maintain linearity, indicating that such a scenario is not possible. The conclusion drawn is that a linear dielectric requires an external field to achieve polarization without violating fundamental principles.

PREREQUISITES
  • Understanding of linear dielectrics and their properties
  • Familiarity with electric field and polarization concepts
  • Knowledge of permittivity (\(\epsilon\)) and vacuum permittivity (\(\epsilon_{0}\))
  • Basic grasp of vector notation in physics
NEXT STEPS
  • Study the relationship between electric field and polarization in linear dielectrics
  • Explore the implications of non-linear dielectric materials
  • Investigate the role of external electric fields in dielectric polarization
  • Learn about Maxwell's equations and their application in dielectric materials
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Physicists, electrical engineers, and students studying electromagnetism or materials science who seek to understand the principles of dielectric polarization and its limitations.

neworder1
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Suppose we have a ball made of linear dielectric with permittivity \epsilon, with some initial homogenous polarization \vec{P} aligned with z axis. Then we know that inside the ball the polarization generates an electric field \vec{E}=\frac{-1}{3\epsilon_{0}}\vec{P} (standard calculation). But we also know that in a linear dielectric we have the relation \vec{P}=(\epsilon - \epsilon_{0})\vec{E}, and these two equations lead to contradiction since we have \vec{E}=\frac{-1}{3\epsilon_{0}}\vec{P} = \frac{-1}{3\epsilon_{0}}(\epsilon - \epsilon_{0})\vec{E}. Does it mean that a linear dielectric can't be polarized this way without an external field?
 
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neworder1 said:
Suppose we have a ball made of linear dielectric with permittivity \epsilon, with some initial homogenous polarization \vec{P} aligned with z axis. Then we know that inside the ball the polarization generates an electric field \vec{E}=\frac{-1}{3\epsilon_{0}}\vec{P} (standard calculation). But we also know that in a linear dielectric we have the relation \vec{P}=(\epsilon - \epsilon_{0})\vec{E}, and these two equations lead to contradiction since we have \vec{E}=\frac{-1}{3\epsilon_{0}}\vec{P} = \frac{-1}{3\epsilon_{0}}(\epsilon - \epsilon_{0})\vec{E}. Does it mean that a linear dielectric can't be polarized this way without an external field?

Yeah, of course! If there is no field, and the object is polarized... it's not a linear material.
 

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