I Faraday's Law Equation: Derivative vs Delta

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    Faraday's law Law
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The discussion centers on the two forms of Faraday's Law: ε=-(dΦB)/(dt) and ε=-(ΔΦB)/(Δt). The first equation represents the instantaneous rate of change of magnetic flux, while the second is an approximation used when the change is relatively constant over a time interval. Both forms are considered equivalent under specific conditions, particularly when the rate of change is stable. The approximation is useful for practical calculations in scenarios where precision is less critical. Understanding these nuances is essential for applying Faraday's Law effectively in physics.
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My textbook gives the equation for Faraday's Law as ε=-(dΦB)/(dt) , the derivative of magnetic flux with respect to time. I have also seen Faraday's law expressed as ε= -(ΔΦB)/(Δt). Are these two forms equivalent? Thanks!
 
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You can take them equivalent.
 
The latter is an approximation to the former. It's only valid when the rate of change is constant, or close enough that you don't care.
 
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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