Magnitude of the induced current in the loop

AI Thread Summary
To find the magnitude of the induced current in a rectangular conducting loop near a long straight wire, the magnetic field generated by the wire must be considered, which varies with distance. The magnetic field is given by the equation B = (μ*I)/(2π*d), where d is the distance from the wire to the loop. Since the magnetic field is not constant across the loop, integration is necessary to calculate the total magnetic flux through the loop. The change in magnetic flux over time will allow for the application of Faraday's law of electromagnetic induction to determine the induced current. Understanding these principles is essential for solving the problem effectively.
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Homework Statement



A rectangular conducting loop of dimensions l×w and resistance R rests in the plane of a long
straight wire as shown. The closest edge of the loop is a distance a from the wire. The current in
the wire is in the upward direction and increases at a constant rate from I to 3I in time Δt.
Find the magnitude of the induced current in the loop.

Homework Equations


Maybe magnetc flux equation ABcos(theta) and magnetic field of a wire = (u*I)/(2*pi*d)

The Attempt at a Solution



Used magnetic field equation (not sure what to use for d) and don't know what to do from there.
 
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The magnetic field varies with the distance from the wire, so the magnetic field through the loop isn't a constant. That means you can't simply take some value for B and multiply it by the total area of the loop to find the total flux. You're going to have to integrate.
 
But we are trying to find the induced current. How do we come about that?
 
That's a good question. What do you think?
 
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