Amperes Law conceptual confusion.

In summary, Amperes Law states that the integral of magnetic field along a closed loop is equal to the product of permeability and enclosed current. However, there are some cases where the magnetic field is present even without an enclosed current, such as the Earth's magnetic field causing a compass to point north. In the case of a toroid, the magnetic field outside is 0 due to no enclosed current, but it is possible to have an amperian path larger than the toroid itself. This raises questions about the absence of a magnetic field with no enclosed current, as in the case of the Earth's magnetic field.
  • #1
Eats Dirt
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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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  • #2
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).
 
  • #3
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.
 

Related to Amperes Law conceptual confusion.

1. What is Amperes Law and how does it relate to electricity and magnetism?

Amperes Law is a fundamental law in electromagnetism that relates the magnetic field produced by a current-carrying wire to the current itself. It states that the magnetic field around a closed loop is directly proportional to the current passing through the loop. This law is a crucial component in understanding the relationship between electricity and magnetism.

2. How is Amperes Law different from Faraday's Law of Induction?

While Amperes Law relates the magnetic field to the current, Faraday's Law of Induction relates the electric field to the changing magnetic field. In other words, Amperes Law deals with the production of magnetic fields through electric currents, while Faraday's Law deals with the production of electric fields through changing magnetic fields.

3. Can Amperes Law be applied to all types of currents?

Yes, Amperes Law can be applied to all types of currents, whether they are steady currents or time-varying currents. However, the form of the law may differ slightly depending on the type of current.

4. Are there any limitations to Amperes Law?

Amperes Law is a macroscopic law and does not take into account quantum effects. It also does not apply to situations where the magnetic field is changing rapidly in time, as it assumes a steady state. Additionally, the law is only valid in situations where the current is confined to a closed loop.

5. How can I use Amperes Law in practical applications?

Amperes Law is commonly used in the design and analysis of electrical circuits, motors, and generators. It is also used in the study of electromagnetic fields, such as in the design of MRI machines. Understanding and applying Amperes Law is crucial for engineers and scientists working in the field of electromagnetism.

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