Amperes Law conceptual confusion.

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SUMMARY

The discussion centers on Ampere's Law, specifically the equation ∫Bdl=μIenc, and its implications in different scenarios. A participant expresses confusion regarding the presence of a magnetic field on Earth, as indicated by a compass, despite the absence of enclosed current (Ienc). Additionally, the conversation addresses the magnetic field behavior around a toroid, where it is established that outside the toroid, the magnetic field is zero due to Ienc being zero. The participant clarifies their understanding of how a compass, acting as a dipole, aligns with the Earth's magnetic field.

PREREQUISITES
  • Understanding of Ampere's Law and its mathematical representation.
  • Familiarity with magnetic fields and their sources.
  • Knowledge of magnetic dipoles and their behavior in external fields.
  • Concept of enclosed current (Ienc) in relation to magnetic fields.
NEXT STEPS
  • Study the derivation and applications of Ampere's Law in various geometries.
  • Explore the concept of magnetic dipoles and their alignment in external magnetic fields.
  • Investigate the magnetic field characteristics of toroidal structures in detail.
  • Learn about the Earth's magnetic field and its interaction with magnetic materials.
USEFUL FOR

Physics students, electrical engineers, and anyone interested in electromagnetism and magnetic field theory.

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For amperes law it is stated that:

∫Bdl=μIenc


My confusion is that B is that for example here now on Earth if I have a compass. It interacts with a the magnetic field of the Earth and points north. There is no I-enclosed yet there is still a magnetic field?


Also another Amperes Law question involving a toroid:

Outside of a toroid it is stated that the magnetic field is 0 because Ienc is 0. Can you not enclose current if your amperian path is larger than the toroid itself?
 
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Ok I understand now for the toroid, how the current negates itself but am still having trouble understanding how there apparently there is no magnetic field with no Ienc (with the compass question).
 
I think that in the Earth magnetic field question, you have a magnetic field which you don't care how was created.
You have a small dipole, your compass.
The dipole moment of the compass tends to allign with the terrestial magnetic field and thus points north.
 

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