Faraday's law of electromagnetic induction

AI Thread Summary
The discussion focuses on applying Faraday's law of electromagnetic induction to a circular coil with specific parameters, including its turns, radius, and resistance. The user calculated the electromotive force (emf) as 1.3696 V but is struggling to derive the magnetic field at the center of the coil produced by the induced current. They attempted to calculate the current using Ohm's law and then used a formula to find the magnetic field, but their results differ from expected values. Participants in the discussion encourage sharing calculations to identify potential errors, emphasizing the importance of verifying each step in the process. The conversation highlights the complexities of electromagnetic induction and the calculations involved.
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Homework Statement




A flat circular coil with 139 turns, a radius of 5.74 x 10-2 m, and a resistance of 0.502 Ω is exposed to an external magnetic field that is directed perpendicular to the plane of the coil. The magnitude of the external magnetic field is changing at a rate of ΔB/Δt = 0.952 T/s, thereby inducing a current in the coil. Find the magnitude of the magnetic field at the center of the coil that is produced by the induced current.

Homework Equations



Faraday's Law of Electromagnetic induction:
emf = -N(delta feta/delta time)

The Attempt at a Solution



I calculated the emf according to the Faraday's Law of Electromagnetic induction as 1.3696 V. But I do not know how to derive the magnetic field at the center of the coil, and I do not understand why resistance is given in this problem.

Please help!
 
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acidandroid said:

Homework Statement




A flat circular coil with 139 turns, a radius of 5.74 x 10-2 m, and a resistance of 0.502 Ω is exposed to an external magnetic field that is directed perpendicular to the plane of the coil. The magnitude of the external magnetic field is changing at a rate of ΔB/Δt = 0.952 T/s, thereby inducing a current in the coil. Find the magnitude of the magnetic field at the center of the coil that is produced by the induced current.

Homework Equations



Faraday's Law of Electromagnetic induction:
emf = -N(delta feta/delta time)

The Attempt at a Solution



I calculated the emf according to the Faraday's Law of Electromagnetic induction as 1.3696 V. But I do not know how to derive the magnetic field at the center of the coil, and I do not understand why resistance is given in this problem.

Please help!

The emf plus the resistance in the wire produce a finite current that you can calculate, right?

Does this current produce a magnetic field?
 
So I did I=E/R to calculate current, then used B=(4pi*10^-7)*I/2*pi*r to get magnetic field but still it's different from the answer. :( I'm just stuck.


G01 said:
The emf plus the resistance in the wire produce a finite current that you can calculate, right?

Does this current produce a magnetic field?
 
acidandroid said:
So I did I=E/R to calculate current, then used B=(4pi*10^-7)*I/2*pi*r to get magnetic field but still it's different from the answer. :( I'm just stuck.

That's the right idea.

I can't help find a mistake if I can't see your work. Please post your calculation.
 
Okay so...

emf= -N A cos 0 (change in B/change in t)
=-139 turns*(0.01035 m^2)*1*(0.952 T/S)
=-1.3696 V

I=E/R
=-1.3696 V/ 0.502 ohm
=-2.728

B=N*(4pi*10^-7)*I/2R
-this is the equation for the magnitude of the magnetic field at the center of a flat circular loop consisting of N turns, each of radius R.
=139*(4pi*10^-7)*-2.728/2*(5.74*10^-2)
=-.00415 TStill a wrong answer. I don't know where to go from here.
G01 said:
That's the right idea.

I can't help find a mistake if I can't see your work. Please post your calculation.
 
Your work seems fine to me. How do you know the answer is wrong?
 

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