Why Electric Flux \Phi is Defined

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Electric flux \Phi is defined as EAcos\theta to represent the projection of the electric field E through a surface area A. The cosine factor accounts for the angle \theta between the electric field and the normal to the surface, affecting the amount of field passing through. This concept is similar to counting the number of bugs hitting a tilted windscreen, where the impact decreases as the angle increases. The mathematical representation of flux involves the dot product of the electric field and the differential area vector. Understanding this definition is crucial for applying Gauss's law in physics.
yaik
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Why the electric flux \Phi is defined as EAcos\theta?

I don't understand the part about cos\theta...
 
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Welcome to PF!

Hi yaik! Welcome to PF! :smile:

Imagine you want to know the flux of bugs flying horizontally along a road.

If you count the number that go splat on your windscreen, then you'll collect less (in a given time) if the windscreen is tilted: the number will be greatest at 90º, and zero at 0º: it'll be proportional to cosθ. :smile:

Mathematically, flux of a field E through a surface with area A is E.(Añ), where ñ is the unit vector normal (perpendicular) to the surface. :wink:​
 
thx!
 
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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