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In a lot of problems, like a rod rotating in a constant magnetic field $B$, we find the EMF induced by the movement by defining an imaginary surface in which the rod is a part of it.

Then we apply Faraday's law and by the rate of change of the magnetic flux through this surface we find the potential difference between two points in this rod.

When I asked why making the surface imaginary is allowed, I got an answer like "Magnetic field lines are closed, so the flux rate of change is the same in all the imagined surfaces" but I just don't get it.

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  • $\begingroup$ What else would you do? You are considering the field at a collection of points in space that make up a surface. I don't understand what you mean by "how is it allowed?" Why are you allowed to consider a rotating rod that isn't actually present near you when solving the problem? $\endgroup$ Commented May 21, 2019 at 17:29

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Fields fill all of space. A vector field therefore has a flux through any surface, regardless of whether that surface corresponds to anything else physical. Even an “imaginary” surface is a surface where the field exists and obeys various physical laws.

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  • $\begingroup$ A vector field therefore has a flux through any surface, regardless of whether that surface corresponds to anything else physical Some physical surfaces would alter or essentially stop any flux. This statement and entire question feels off to me. When using these laws we really are just considering mathematical surfaces. It doesn't make sense to think about constructing surfaces with materials? I don't know, I can't seem to say what I am thinking in the right way. Oh well, still a +1 from me $\endgroup$ Commented May 21, 2019 at 17:35
  • $\begingroup$ I didn’t mean to imply a nonzero flux. Zero is a valid value for a field and a flux, such as when the surface is inside a conductor. $\endgroup$
    – G. Smith
    Commented May 21, 2019 at 17:40
  • $\begingroup$ Sorry, I wasn't trying to say that either. I guess the question doesn't make sense to me. We have a field at all points in space. We have laws that are expressed as equations that involve mathematical surfaces. I just don't understand what other option there is. It's not like we solve the equation by building (in our minds?) some sort of physical surface to determine the flux through. $\endgroup$ Commented May 21, 2019 at 17:51
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    $\begingroup$ The OP may still be in the process of making the conceptual leap from thinking about particles of matter to thinking about fields, and how that means physics is actually “going on” everywhere. $\endgroup$
    – G. Smith
    Commented May 21, 2019 at 18:00
  • $\begingroup$ Now that i rethink of the question, it was pretty obvious in terms of fields and maxwell equations and not like matter and interactions between them, i may consider deleting it. Thank you so much for answering anyway. $\endgroup$ Commented May 21, 2019 at 18:18

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