- #1
giladsof
- 13
- 0
What is the impact of superposition on Amper's Law?
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Homework Help Overview
The discussion revolves around the application of Ampère's Law in the context of superposition, particularly concerning the magnetic fields generated by currents in different directions within a cylindrical setup.
Discussion Character
- Exploratory, Conceptual clarification, Mathematical reasoning
Approaches and Questions Raised
- Participants explore the use of Amperian loops to analyze the magnetic field inside and outside a cylinder with opposing currents. Questions arise regarding the correctness of interpretations and the implications of infinite conductors.
Discussion Status
Some participants have provided insights into the reasoning behind the application of Ampère's Law and the concept of enclosed current, while others express uncertainty about the initial interpretations and seek clarification on mistakes made.
Contextual Notes
There is a mention of the assumption that the conductors are infinite, which may influence the application of Ampère's Law in this scenario.
- #2
Mandeep Deka
- 103
- 0
what is your question?
- #3
giladsof
- 13
- 0
this is the wrong answer... the question is where is my mistake...?
- #4
silmaril89
- 85
- 0
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
- 13
- 0
Cheers... very helpful...
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