B field of a wire carrying AC current

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SUMMARY

The discussion focuses on calculating the magnetic field around a wire carrying an AC current of 495Hz at 8Vpp and 0.8mA. The initial approach using Ampere's Law was inadequate due to the need for Maxwell's corrections when dealing with time-varying fields. It is established that for distances close to the wire relative to the signal's wavelength, Ampere's Law can be applied. However, for more distant calculations, solving Maxwell's equations as non-homogeneous wave equations is necessary, utilizing techniques such as Green's functions.

PREREQUISITES
  • Understanding of Ampere's Law and its applications
  • Familiarity with Maxwell's equations and their implications
  • Knowledge of AC circuit theory and signal characteristics
  • Basic proficiency in solving differential equations, particularly wave equations
NEXT STEPS
  • Study the application of Ampere's Law in AC circuits
  • Learn about Maxwell's equations and their corrections for time-varying fields
  • Research the use of Green's functions in solving wave equations
  • Explore the relationship between electric and magnetic fields in AC systems
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Electrical engineers, physicists, and students studying electromagnetism, particularly those interested in the behavior of magnetic fields around AC current-carrying conductors.

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Hi. New to the forums so bear with me.

I am trying to calculate the magnetic field at a distance r from a wire carrying a 495Hz signal at 8Vpp and current 0.8mA. Initially I tried ampere's law, but fell into the trap of using the un-modified form (without maxwell's correction). I know that the field changes with the frequency, but I am unsure of exactly how they tie together, and I can't seem to find the relationship between dE/dt and frequency.

Any ideas?
 
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you still would use amperes law . your current will be a function of time I(t)
You would only use maxwells correction if you had free charge and if it was changing as a function of time. Like charging up a capacitor. And i don't think you have any free charge.
 
Sorry, it's not that simple. When you have AC currents, you have changing fields, which means that the electric and magnetic fields are coupled. If the distance r you are interested in is very close to the wire compared to the wavelength of the signal, then you you can treat the problem as pseudo-static and just use Ampere's law. Otherwise you have to solve all of Maxwell's equations simultaneously because the fields are coupled. The best way to do this is to transform Maxwell's equations into non-homogenous wave equations and solve using Green functions. See http://faculty.uml.edu/cbaird/95.658%282011%29/Lecture6.pdf" , for example.
 
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