Magnitude of the induced current in the loop

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SUMMARY

The discussion focuses on calculating the magnitude of the induced current in a rectangular conducting loop placed near a long straight wire carrying an increasing current. The wire's current rises from I to 3I over a time interval Δt, necessitating the use of Faraday's law of electromagnetic induction. The magnetic field generated by the wire is described by the equation B = (μ₀I)/(2πd), where d is the distance from the wire to the loop. The solution requires integrating the varying magnetic field across the loop's area to determine the total magnetic flux and subsequently the induced current.

PREREQUISITES
  • Understanding of Faraday's law of electromagnetic induction
  • Familiarity with the magnetic field equation B = (μ₀I)/(2πd)
  • Knowledge of integration techniques for variable fields
  • Concept of magnetic flux and its relation to induced current
NEXT STEPS
  • Study the integration of magnetic fields over a loop area
  • Learn about the application of Faraday's law in varying magnetic fields
  • Explore the concept of induced electromotive force (EMF) in circuits
  • Investigate the effects of changing current on nearby conductive materials
USEFUL FOR

Students studying electromagnetism, physics educators, and anyone interested in the principles of induced currents and magnetic fields in conductive loops.

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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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