Relationships between integration limits of Maxwell Equation

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The discussion centers on the relationship between the integration limits of Maxwell's Equations in their integral form and their differential counterparts. It highlights that transitioning from integral to differential forms involves applying Stokes' and Gauss' Theorems, which relate line and surface integrals to pointwise operations. The integration limits are crucial for understanding how these equations describe electromagnetic phenomena at different scales. The differential form is considered more fundamental in modern physics. Overall, the conversation emphasizes the mathematical foundations that connect these forms of Maxwell's Equations.
henrybrent
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I don't understand the relationships between the integration limits of Maxwell Equations (specifically the ones in integral form in matter)

Is this related to Stokes/Gauss' Theorems? or something else?
 
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What to you mean by integration limits? The Maxwell equations in integral form lead to those in differential form by taking the appropriate limits, using the definitions of the differential operators curl and div through line and surface integrals, which are contracted to a point. From a modern point of view, the differential form of the Maxwell equations are the most natural form of the laws underlying electromagnetic phenomena.
 
Would you say that's basically what Stokes/Divergence thereom is?
 
Thread 'Motional EMF in Faraday disc, co-rotating magnet axial mean flux'

Thread 'Motional EMF in Faraday disc, co-rotating magnet axial mean flux'

So here is the motional EMF formula. Now I understand the standard Faraday paradox that an axis symmetric field source (like a speaker motor ring magnet) has a magnetic field that is frame invariant under rotation around axis of symmetry. The field is static whether you rotate the magnet or not. So far so good. What puzzles me is this , there is a term average magnetic flux or "azimuthal mean" , this term describes the average magnetic field through the area swept by the rotating Faraday...
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