Why is induced electric field circular?

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Discussion Overview

The discussion centers on the nature of the induced electric field in the context of time-varying magnetic fields, exploring why this electric field is circular or forms closed loops. The scope includes theoretical aspects of electromagnetism, particularly relating to Faraday's law and Maxwell's equations.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants assert that a time-varying magnetic field induces a circular electric field due to the non-conservative nature of the fields, governed by Faraday's and Maxwell's laws.
  • One participant mentions that the induced electric field is related to the change in magnetic flux associated with a loop, as expressed by the equation ∫ E⋅dl=dΦB/dt.
  • Another participant introduces the concept that any vector field can be decomposed into irrotational and solenoidal parts, noting that the solenoidal part corresponds to the time variation of the magnetic field.
  • A later reply emphasizes the need to understand how the time-variation of the magnetic field leads to the rotation of the electric field, rather than just its divergence.
  • One participant references Faraday's law, stating that the circular component of the electric field is equal to the change in the magnetic field over time, represented by the equation ∇ × E = ∂B/∂t.

Areas of Agreement / Disagreement

Participants express differing views on the mechanisms behind the circular nature of the induced electric field, with some focusing on the mathematical descriptions while others seek a more intuitive understanding. The discussion remains unresolved regarding the precise reasoning behind the circular shape of the electric field.

Contextual Notes

Participants have not fully resolved the assumptions regarding the relationship between the magnetic field's time-variation and the characteristics of the induced electric field. There is also a lack of consensus on the interpretation of the terms "irrotational" and "solenoidal" in this context.

turaturer
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Time-varying magnetic field makes electric field circular(or close loop). I am asking the reason why it is circular or close loop shape?
 
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turaturer said:
Time-varying magnetic field makes electric field circular(or close loop). I am asking the reason why it is circular or close loop shape?
The fields are non-conservative. They have to follow the laws of electromagnetism ( discovered by Faraday and Maxwell). In this case, electric field is induced only when there is change in magnetic flux associated with a loop (real or hypothetical).
So,∫ E⋅dl=dΦB/dt.
Since the varying flux is associated with a loop, the electric field lines are circular, i.e. they are along the loop. Everything is governed by Maxwell's mighty equations.
 
turaturer said:
Time-varying magnetic field makes electric field circular(or close loop). I am asking the reason why it is circular or close loop shape?
Any vector field can be decomposed into an irrotational part and a solenoidal part. Faraday discovered that the solenoidal part is equal to the time variation of the magnetic field.
 
DaleSpam said:
Any vector field can be decomposed into an irrotational part and a solenoidal part. Faraday discovered that the solenoidal part is equal to the time variation of the magnetic field.
Thank you. But I asked how time-variation of the magnetic field makes electric field rotate, not make it divergence field.
 
Yes. That is what I answered. "Faraday discovered that the solenoidal part..."

Faradays law says ##\nabla \times E =\partial B/\partial t##. In words this says that the circular part of E is equal to the change of B.
 
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