Confusion with electromagnetism and Faraday's law

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Discussion Overview

The discussion revolves around the concepts of magnetic flux, Gauss's law, and Faraday's law in electromagnetism. Participants explore the implications of these laws on electromotive force (EMF) in both open and closed surfaces, addressing potential confusions regarding the definitions and applications of these principles.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions whether the magnetic flux being zero around a closed loop, as stated by Gauss's law for magnetostatics, implies that the EMF around any closed loop is also zero.
  • Another participant clarifies that Gauss's law involves a closed surface integral, while Faraday's law involves an open surface integral, emphasizing the importance of the time derivative of the flux in Faraday's law.
  • A participant expresses confusion about the implications of taking the time derivative out of the integral, suggesting that if zero is integrated over a closed circuit, it implies a constant EMF regardless of changes in the magnetic field, which seems counterintuitive.
  • Another participant points out that Faraday's law applies to an open surface and questions the relevance of considering a closed circuit in this context.

Areas of Agreement / Disagreement

Participants generally agree on the definitions of Gauss's law and Faraday's law, but there remains disagreement and confusion regarding the implications of these laws when applied to closed circuits versus open surfaces. The discussion is unresolved regarding the interpretation of EMF in these scenarios.

Contextual Notes

Participants express uncertainty about the relationship between the magnetic field changes and the resulting EMF, particularly when considering the integration of zero over a closed circuit. There are also assumptions about the nature of the surfaces involved in the laws being discussed.

Physgeek64
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Hi- Sorry if this is a silly question, but by definition the magnetic flux is given by integral B dot dA. But From Gauss' law for magnetostatics is this not zero around a closed loop? So would that not then imply that the EMF around any closed loop is zero? Obviously I'm missing something, so I would be really grateful for any clarification.

Thanks in advance :) you guys rock
 
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In Gauss's law, the surface integral is over a closed surface. In Faraday's law, the surface integral for the flux is over an open surface.

Also, note that Faraday's law uses the rate of change of the flux through the surface (i.e. the time derivative of the surface integral), not the flux itself. At a particular point in time, it's possible for the flux to be instantaneously zero, but increasing or decreasing. And it's possible for the flux to be nonzero but constant (time derivative is zero).
 
jtbell said:
In Gauss's law, the surface integral is over a closed surface. In Faraday's law, the surface integral for the flux is over an open surface.

Also, note that Faraday's law uses the rate of change of the flux through the surface (i.e. the time derivative of the surface integral), not the flux itself. At a particular point in time, it's possible for the flux to be instantaneously zero, but increasing or decreasing. And it's possible for the flux to be nonzero but constant (time derivative is zero).

Thanks for the reply. That makes sense, but my real problem is that the time derivative can be taken out of the integral meaning that 0 is being integrated over a closed circuit ( I get that Faradays Law is for an open surface, but for arguments sake consider a closed circuit) then this implies that the rate of change of flux, and hence the EMF is constant regardless of how the magnetic field is changing. This seems counter intuitive since if it were changing rapidly and randomly I'd expect a different EMF to when the field is changing slowly and periodically.

Thanks again :)
 
Physgeek64 said:
I get that Faradays Law is for an open surface, but for arguments sake consider a closed circuit

In Faraday's law, the EMF is the integral of the induced ##\vec E## around the boundary (edge) of an open surface. If the surface is closed, where's the boundary?
 

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