Understanding Ampere's Law: Clarifying the Role of External Currents

In summary, Ampere's Law states that the line integral of a magnetic field along a closed path is equal to the current passing through the enclosed area. This means that when solving for a magnetic field, we are only considering the current within the enclosed path. Any current outside of this path will still contribute to the total magnetic field, but it is not solely responsible for creating the magnetic field described by Ampere's Law. This clarification also helps understand Gauss's Law.
  • #1
maccha
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I can't seem to understand why a current outside of a loop doesn't contribute in Ampere's Law? Any clarification would be appreciated.
 
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  • #2
In integral form Ampere's law says that the line integral of a magnetic field of a closed path is equal to the current that passes through that enclosed path.

When we solve for a magnetic field we are solving for a magnetic field that is made up of only the enclosed current.

So if there is a current somewhere outside of the enclosed path it will contribute to the total magnetic field, however that is different than the magnetic field that is created solely from an enclosed current which is the magnetic field of ampere's law.
 
  • #3
Ohh that just clarified things for Gauss's Law too! Thank you!
 

1. What is Ampere's Law?

Ampere's Law is a fundamental law in electromagnetism, which states that the magnetic field created by an electric current is proportional to the electric current and the distance from the current.

2. How is Ampere's Law used in real life?

Ampere's Law is used in many practical applications, such as motors, generators, and transformers. It is also used to calculate the magnetic fields of wires and solenoids.

3. What is the mathematical formula for Ampere's Law?

The mathematical formula for Ampere's Law is B = μ₀I/2πr, where B is the magnetic field, μ₀ is the permeability of free space, I is the electric current, and r is the distance from the current.

4. How does Ampere's Law relate to Gauss's Law?

Ampere's Law and Gauss's Law are both fundamental laws in electromagnetism. While Ampere's Law deals with the relationship between electric currents and magnetic fields, Gauss's Law deals with the relationship between electric charges and electric fields.

5. Can Ampere's Law be used to calculate the magnetic field of any current-carrying wire?

Yes, Ampere's Law can be used to calculate the magnetic field of any current-carrying wire as long as the wire is straight and the current is constant. For more complex situations, such as a wire with varying current, other methods such as Biot-Savart Law may be used.

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