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

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Homework Help Overview

The discussion revolves around finding the induced electromotive force (emf) in a scenario involving current and motion, with a focus on the magnetic field and its effects. The problem appears to involve concepts from electromagnetism, particularly magnetic flux and its relation to changing areas and currents.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants express confusion regarding the relationship between the magnetic field's non-uniformity and the rate of change of flux. There are attempts to integrate the magnetic field over an area to find magnetic flux, but uncertainty remains about the appropriateness of this method.
  • One participant questions whether substituting the radius in the magnetic field equation with area for integration is valid, while another notes the challenge of obtaining a time-dependent function for differentiation.
  • There is also a query about the potential need for a double integral, indicating a search for clarity on the mathematical approach required.

Discussion Status

The discussion is ongoing, with participants actively exploring different mathematical approaches and questioning their assumptions. Some guidance has been offered regarding the integration of the magnetic field, but no consensus has been reached on the correct method or interpretation of the problem.

Contextual Notes

Participants are grappling with the implications of resistance in the context of the problem, and there is a mention of multiple questions that may be related to the main inquiry. The original poster's confusion about the relationship between magnetic flux and the geometry of the problem is evident.

1MileCrash
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Homework Statement



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Homework Equations





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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