Induced EMF in Coaxial Loops: Calculating Separation Distance

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The discussion focuses on calculating the separation distance between a large coaxial loop and a small loop experiencing induced electromotive force (emf). A large loop with a radius of 1 meter is driven by a linearly increasing current, inducing an emf of 983 nV in a smaller loop with a radius of 5 centimeters positioned nearby. Participants suggest using the Biot-Savart law for calculating the magnetic field due to the large loop, as the increasing current complicates the use of simpler equations. They emphasize the importance of considering the geometry of the loops and the magnetic field's direction when applying Faraday's law to find the induced emf. The conversation concludes with a confirmation that the proposed approach using Faraday's law and Biot-Savart is valid for determining the separation distance.
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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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