Find induced emf (among other things) in this current + motion

AI Thread Summary
The discussion revolves around finding the induced electromotive force (emf) in a scenario involving magnetic fields and motion. The poster expresses confusion about the relevance of the magnetic field's non-uniformity and the correct approach to calculating magnetic flux. They consider using integrals to determine the magnetic field per unit area but struggle with the application and integration process. Questions arise about the role of resistance in the calculations and whether the magnetic field equation can be integrated effectively. Overall, the poster is seeking clarity on the appropriate mathematical methods to solve the problem.
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The Attempt at a Solution



I'm pretty confused about this one.

First, I thought that maybe the magnetic field's non uniformity didn't matter since the rate of change of flux was going to be the rate of change of area, but that's wrong.

So I thought I should do some kind of integral to figure out the magnetic field from the top to bottom "per unit area" but that doesn't even make sense.

So then I decided to find the magnetic flux by integrating B dA but that still doesn't make much sense to me.

What do I do?

And what does resistance have to do with it? Or is that for one of the lower questions?
 

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In the integral for B dA, can I write the equation for B (mu 0 * i / 2piR) and replace R with the area for that R and integrate? Does that work?
 
But that still won't get me a function of t so that I can differentiate to find rate... and R is constant anyway.

Very confused now.
 
Is it some kind of double integral?
 

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