Faraday induction in constant B field, with non-conduction wires

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SUMMARY

The discussion focuses on Faraday's law of induction in a constant magnetic field (B field) with a conducting loop that expands at a constant rate. The induced electromotive force (EMF) is calculated using the formula E = Bv, where v represents the velocity of area expansion. The inquiry centers on the scenario where the wire is a perfect insulator, questioning whether the same EMF occurs and if polarization in the dielectric material results. The conversation highlights the implications of Maxwell's curl equations and the behavior of charges under Lorentz force in a dielectric medium.

PREREQUISITES
  • Understanding of Faraday's law of induction
  • Familiarity with Maxwell's equations
  • Knowledge of dielectric materials and polarization
  • Basic principles of electromagnetism
NEXT STEPS
  • Explore the implications of Faraday's law in non-conductive materials
  • Study the behavior of dielectric materials under electromagnetic fields
  • Investigate the relationship between induced EMF and charge polarization
  • Review advanced concepts in Maxwell's equations and their applications
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Physicists, electrical engineers, and students studying electromagnetism, particularly those interested in the behavior of materials in electromagnetic fields and the principles of induction.

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A standard textbook problem features a constant B field and a conducting loop that increases in area at constant rate.
It is easy to work out the induced EMF and the associated electric field magnitude and direction (CW or CCW). The magnitude of the E field
is E = B v where v is a velocity. The current in the loop is easy to work out and the rate of dissipation (I^2 R) compared with the external work/power needed to keep the loop area expanding at a constant rate.

My question is: What if the wire is actually a perfect insulator? Will there still be the same EMF and will that induce polarization in the dielectric
insulating material? There will be no current so, apparently, so no induced magnetic field thus no rate of change of magnetic field.
How is that consistent with the differential form of Maxwell's curl equations?
 
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When the wire is made larger the positive and negative charges are moved raadially and feel opposite tangential forces frrom Lorentz force. I would expect polarization in a polarizeable dielectric material
 
If the "wire" is a dielectric you'll also have the said EMF, which will polarize the wire.
 

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