Electric Eddy Field: Calculating with Maxwell's Equations

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SUMMARY

The discussion centers on the calculation of electric fields using Maxwell's equations, specifically addressing the role of scalar and vector potentials. The formulas E = -∇Φ - ∂A/∂t and B = rot A are highlighted for deriving electric and magnetic fields. The term "electric eddy field" is clarified as non-standard; instead, the focus should be on the electric field itself. The relationship between the time derivative of A and the induced electric field due to a time-varying magnetic field is emphasized through the application of Maxwell's equations.

PREREQUISITES
  • Understanding of Maxwell's equations
  • Familiarity with vector calculus concepts such as gradient and curl
  • Knowledge of scalar and vector potentials
  • Basic principles of electromagnetism
NEXT STEPS
  • Study the derivation of Maxwell's equations in detail
  • Learn about the physical significance of scalar and vector potentials
  • Explore the implications of time-varying magnetic fields on electric fields
  • Investigate applications of Maxwell's equations in electromagnetic theory
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Students of physics, electrical engineers, and anyone interested in advanced electromagnetism and the application of Maxwell's equations in theoretical and practical scenarios.

hildebrand
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Hello!

I'm studying Maxwell's equations at the moment. To solve Maxwell's equations one can introduce scalar- and vectorpotentials and calculate the electric and magnetic field by [tex]E=-\text{grad}\,\Phi-\frac{\partial A}{\partial t}[/tex]
and
[tex]B=\text{rot}\,A[/tex],
respectively.
I have the following question to that: Is the contribution of the time derivative of [tex]A[/tex] in the formula for [tex]E[/tex] due to the electric eddy field that is induced by a time varying magnetic field? If not, how it is possible to calculate the electric eddy field when a time varying magnetic field is given?

Thank you for your help!
 
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The term "electric eddy field" is not commonly used in English. Just saying "electric field" is enough. If you take
[tex]\text{rot}\,E=\text{rot}[-\text{grad}\,\Phi-\frac{\partial A}{\partial t}][/tex], you get Maxwell's equation that is differential equation relating E and B.
 

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