Why is induced electric field circular?

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SUMMARY

The discussion centers on the phenomenon of induced electric fields being circular due to time-varying magnetic fields, as described by Faraday's Law of Electromagnetic Induction. The key equation, ∫ E⋅dl = dΦB/dt, illustrates that the induced electric field (E) forms closed loops in response to changes in magnetic flux (ΦB). This behavior is governed by Maxwell's equations, specifically highlighting that the solenoidal component of the electric field corresponds to the time variation of the magnetic field (B). The circular nature of the electric field is a direct consequence of these electromagnetic principles.

PREREQUISITES
  • Understanding of Faraday's Law of Electromagnetic Induction
  • Familiarity with Maxwell's equations
  • Knowledge of vector field decomposition (irrotational and solenoidal components)
  • Basic concepts of magnetic flux (ΦB) and its variations
NEXT STEPS
  • Study Maxwell's equations in detail, focusing on their implications for electromagnetic fields
  • Explore the mathematical derivation of Faraday's Law and its applications
  • Investigate the concept of magnetic flux and its role in electromagnetic induction
  • Learn about vector calculus, particularly the concepts of curl and divergence
USEFUL FOR

Students and professionals in physics, electrical engineering, and anyone interested in understanding the principles of electromagnetism and their applications in technology.

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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