Induced Electric Field and Faraday's law

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SUMMARY

The discussion revolves around calculating the induced electric field using Faraday's law in the context of a cylindrical magnet at the Francis Bitter National Magnet Laboratory. The magnet produces a 30 T magnetic field, varying sinusoidally between 29.6 T and 30.9 T at a frequency of 15 Hz. The user initially applied the formula E = (r/2)(dB/dt) but encountered errors in their calculations. The correct approach involves differentiating the magnetic field function with respect to time, incorporating the angular frequency ω = 2π/T.

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  • Understanding of Faraday's law of electromagnetic induction
  • Familiarity with sinusoidal functions and their derivatives
  • Knowledge of angular frequency and its calculation
  • Basic concepts of electromagnetism and electric fields
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  • Study the derivation and application of Faraday's law in various contexts
  • Learn about angular frequency and its role in electromagnetic induction
  • Explore the mathematical treatment of sinusoidal magnetic fields
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DarkWarrior
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Hello, I'm stuck (again) on a physics problem.

The problem:

Early in 1981 the Francis Bitter National Magnet Laboratory at M.I.T. commenced operation of a 3.3 cm diameter cylindrical magnet, which produces a 30 T field, then the world's largest steady-state field. The field magnitude can be varied sinusoidally between the limits of 29.6 and 30.9 T at a frequency of 15 Hz. When this is done, what is the maximum value of the magnitude of the induced electric field at a radial distance of 1.6 cm from the axis?

What I've done so far: I've used Faraday's law, and after messing around with the equation I got E = (r/2)(dB/dt). As I understand it, the induced electric field is inside the magnetic field (r is less than R), so I thought this equation was correct.

R= .0165 m
r = .016 m
dB/dt = 19.5 Tesla/second. Since the frequency is 15, you multiply the difference of 30.9 and 29.6 by 15, getting 19.5

However when I plug the numbers in, my answer comes out wrong. Can someone point out where I screwed up? Thank you!
 
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DarkWarrior said:
Hello, I'm stuck (again) on a physics problem.

The problem:

Early in 1981 the Francis Bitter National Magnet Laboratory at M.I.T. commenced operation of a 3.3 cm diameter cylindrical magnet, which produces a 30 T field, then the world's largest steady-state field. The field magnitude can be varied sinusoidally between the limits of 29.6 and 30.9 T at a frequency of 15 Hz. When this is done, what is the maximum value of the magnitude of the induced electric field at a radial distance of 1.6 cm from the axis?

What I've done so far: I've used Faraday's law, and after messing around with the equation I got E = (r/2)(dB/dt). As I understand it, the induced electric field is inside the magnetic field (r is less than R), so I thought this equation was correct.

R= .0165 m
r = .016 m
dB/dt = 19.5 Tesla/second. Since the frequency is 15, you multiply the difference of 30.9 and 29.6 by 15, getting 19.5

However when I plug the numbers in, my answer comes out wrong. Can someone point out where I screwed up? Thank you!
Set up the equation for the field as a function of time (B = sinusoidal term + constant). Then differentiate with respect to time. There will be a factor \omega = 2\pi/T in the equation.

AM
 

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