How Does Ampere's Law Determine the Ranking of Loops by Enclosed Current?

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SUMMARY

Ampere's Law is utilized to rank loops based on the enclosed current, with the solution identifying loops d and c as tied for the greatest current, followed by loop b, and then loop a. The relevant equations include B = μ₀ I_enc, B = μ₀ i / (2πr) for outside the wire, and B = (μ₀ i / (2πR²)) r for inside the wire. The discussion emphasizes treating current density as uniform across the wire, which clarifies the ranking of the loops. This approach simplifies the problem-solving process, demonstrating that complex methods are often unnecessary.

PREREQUISITES
  • Understanding of Ampere's Law and its applications
  • Familiarity with magnetic field equations related to current-carrying wires
  • Knowledge of current density concepts
  • Basic principles of electromagnetism
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Students of physics, electrical engineers, and anyone interested in understanding the principles of electromagnetism and current distribution in conductors.

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Hellow every one I have small Q but I stuck on it

there is pic attachedhope to be interesting and clear to you

Homework Statement


rank the loops accoroding to the current enclosed greatest first

Homework Equations



we have three eqn's
B = u "node" I encِْْْْ
B = u"node" i / 2 pi r outside the wire
B = (u"node" i / 2 pi R2 ) r inside the wire

The Attempt at a Solution

I knew the solotion but I do not know how did they get it

the soloution is d and c tie then b then a
 

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Hint: Treat the current density as uniform across the wire.
 
thank you very much Doc al it is as what you mentioned related to the current density for c and d the current is the same whereas in b smaller and a is even smaller than b



Sometimes we think in very difficult method when we can solve it in easier way


Thank you again and regards​
 

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