- #1
giladsof
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What is the impact of superposition on Amper's Law?
- Thread starter giladsof
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In summary, the conversation is about a problem involving amperian loops and current enclosed. The correct answer is that the field is zero outside the cylinder and inside the cylinder it is just the first field given. The mistake in the wrong answer may be due to the conductors not being infinite. The amperian trick is used to solve the problem and it is considered very helpful.
- #2
Mandeep Deka
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what is your question?
- #3
giladsof
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this is the wrong answer... the question is where is my mistake...?
- #4
silmaril89
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It's been awhile since I've done a problem like this, so please forgive me if I'm wrong.
The first thing you should do is draw two amperian loops. One inside the cylinder curling in the azimuthal direction with it's center being right where the wire is. The second one should be outside the cylinder with the same direction and same center as the first one.
Now the current in ampere's law is the current ENCLOSED by the amperian loops. So, for the one outside of everything the total current enclosed is zero (since the currents are in opposite directions). For the amperian loop inside the cylinder the current enclosed is I.
Therefore, the answer is, the field is zero outside the cylinder and inside the cylinder it is just the first field you gave (you called it the Wire's magnetic field). Is that the answer you were looking for?
Now, you might wonder why your answer is wrong. And I think they would be right if the conductors were not infinite, but they are and since they are we can use this amperian trick.
The first thing you should do is draw two amperian loops. One inside the cylinder curling in the azimuthal direction with it's center being right where the wire is. The second one should be outside the cylinder with the same direction and same center as the first one.
Now the current in ampere's law is the current ENCLOSED by the amperian loops. So, for the one outside of everything the total current enclosed is zero (since the currents are in opposite directions). For the amperian loop inside the cylinder the current enclosed is I.
Therefore, the answer is, the field is zero outside the cylinder and inside the cylinder it is just the first field you gave (you called it the Wire's magnetic field). Is that the answer you were looking for?
Now, you might wonder why your answer is wrong. And I think they would be right if the conductors were not infinite, but they are and since they are we can use this amperian trick.
- #5
giladsof
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Cheers... very helpful...
Related to What is the impact of superposition on Amper's Law?
What is Amper's Law Superposition?
Amper's Law Superposition is a fundamental law in electromagnetism that describes the relationship between electric currents and magnetic fields. It states that the total magnetic field at a point in space is equal to the sum of the magnetic fields produced by each individual current at that point.
How is Amper's Law Superposition different from the original Amper's Law?
Amper's Law Superposition is an extension of the original Amper's Law, which only applies to steady currents. Amper's Law Superposition applies to both steady and non-steady currents, making it a more comprehensive law.
What is the mathematical expression for Amper's Law Superposition?
The mathematical expression for Amper's Law Superposition is: ∮B•dl = μ0(∑iIi + ε0∂/∂t∫E•dA), where B is the magnetic field, dl is an infinitesimal length element along a closed path, μ0 is the permeability of free space, Ii is the current through each individual wire, ε0 is the permittivity of free space, t is time, and E is the electric field.
What are some practical applications of Amper's Law Superposition?
Amper's Law Superposition is used in a variety of practical applications, including electromagnets, motors, generators, and transformers. It is also used in the design and analysis of electronic circuits and devices.
What are the limitations of Amper's Law Superposition?
Amper's Law Superposition assumes that the magnetic field produced by each individual current is independent of the presence of other currents. This is not always the case, and in situations where the magnetic fields interact, the superposition principle may not hold. Additionally, it only applies to static electric fields and does not take into account any non-electromagnetic forces acting on the charges.
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