Induced potential - when do you have to consider EM waves?

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SUMMARY

The discussion centers on the induced electric potential in a second conductor due to a 60 Hz AC current flowing through a first conductor. The Biot-Savart Law can be applied to calculate the magnetic field (B), and subsequently, Faraday's Law can determine the induced electric potential. However, the presence of electromagnetic (EM) waves generated by the alternating current introduces additional considerations. The quasi-static approximation is deemed valid in this scenario since the wavelength of the 60 Hz EM waves is significantly larger than the distance between the conductors, allowing for the neglect of the induced potential from EM waves.

PREREQUISITES
  • Understanding of Biot-Savart Law
  • Familiarity with Faraday's Law of Electromagnetic Induction
  • Knowledge of electromagnetic wave propagation
  • Concept of quasi-static approximation in electromagnetism
NEXT STEPS
  • Study the application of Biot-Savart Law in various configurations
  • Explore Faraday's Law in the context of AC circuits
  • Investigate the characteristics of electromagnetic waves at different frequencies
  • Review the implications of the quasi-static approximation in practical scenarios
USEFUL FOR

Electrical engineers, physicists, and students studying electromagnetism, particularly those interested in the effects of alternating currents and electromagnetic wave interactions.

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There's a long conductor carrying a 60 hz AC current. There's a second conductor parallel to the first current carrying conductor, and a hundred meters away from it.

I want to know what the electric potential induced by the changing B field is in the second conductor.

Theoretically I could use the biot-savart law to calculate B and then Faraday's law to calculate the induced electric potential from the changing B. However the alternating current also produces EM waves whose B field would induce an electric potential separate from that calculated by the biot-savart law as described above.

Is it justifiable to ignore the electric potential induced by the EM waves? Why/why not? Or am I just confused?
 
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The usual rule of thumb is that you can use a "quasi static" approximation whenever the length scales are small compared to the wavelength of the EM waves. At 60 Hz the wavelengths are so much larger than 100 m that the quasi static approximation should be fine.

See this textbook, especially ch 8
http://web.mit.edu/6.013_book/www/book.html
 
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