Induced EMF in Coaxial Loops: Calculating Separation Distance

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Homework Help Overview

The discussion revolves around calculating the separation distance between two coaxial loops, one large and one small, where the large loop carries a linearly increasing current, inducing an electromotive force (emf) in the small loop. The problem involves concepts from electromagnetism, specifically related to induced emf and magnetic fields.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore the use of the Biot-Savart law and Faraday's law to relate the induced emf to the magnetic field generated by the large loop. Questions arise regarding the appropriate equations to use, particularly in the context of an increasing current and the geometry of the loops.

Discussion Status

There is an ongoing exploration of different methods to calculate the magnetic field and induced emf. Some participants suggest using numerical integration with the Biot-Savart law, while others discuss the limitations of applying Ampere's law in this scenario. Guidance has been offered regarding the use of specific equations and the nature of the magnetic field in relation to the loops.

Contextual Notes

Participants note the complexity introduced by the increasing current and the need to consider the geometry of the loops when calculating the magnetic field. There is also mention of potential numerical methods for integration, indicating a preference for computational approaches over simpler analytical methods.

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1. A very large loop of metal wire with radius 1meter is driven with a linearly increasing current at a rate of 200amps/second . A very small metal wire loop with radius 5centimeter is positioned a small distance away with its center on the same axis (the loops are coaxial). The small loop experiences an induced emf of 983nV . What is the separation of the loops in meters

Homework Equations

3. I tried to use Biot-Savart law to find the produced B but it is not right because of the increasing current,
Could you explain me the equations to use?
Thanks.
 
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If you calculate the flux, ψ, through the small loop some distance away, at say 200A in the large loop, you know dψ/dt through the small loop.

Flux = the integral of B*dx*dy over the surface surrounded by the small loop.

Emf = dψ/dt.

Remember that when the centers of the loops are at som distance, the B-field is not overall perpendicular to a flat surface in the small loop.
 
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Is the magnetic field produced by the large loop B=(muo*I)/(2*pi*r)?
 
At a specific point: No, not in this case.

You are using Amperes law, that says: The circulation integral: ∫ H⋅ds = N*I. (In vacuum B = μ0 * H). So Amperes Law says nothing about the magnetic field at a specific location. But you can use Amperes law under symmetrical conditions, e.g. a long linear conductor. Biot-Savart works fine here.

So you must think out a way of using Biot-Savart (find some symmetri around the centeraxis of the loops): If you have calculated B at a point outside the centeraxis, then all points at the same distance from the axis and same distance from the large loop will have the same perpendicular strength through the small loop.

As all data have physical values (not algebraic) you may develop a program, taking care of a numerical integration using Biot-Savart. ( Don't use excel here, it will never end).
 
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If i use Faraday's law emf induced=-d(phi)/dt i could find B and by using Bior-Savart law on axis of a current loop , i would be abble to find thr separation between the loops?
 
Yes it was good , thanks a lot Hesch for your help.
 

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