Ampere's Law and Conductor: Finding ∫B.dl for a Semicircle in the x-z Plane

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Homework Help Overview

The problem involves applying Ampere's Law to a semicircular conductor carrying current in the x-y plane and finding the line integral of the magnetic field around a circular path in the x-z plane. Participants are exploring the implications of current distribution and the conditions under which Ampere's Law can be applied.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the necessity of completing the circuit to apply Ampere's Law and question the implications of the semicircular current alone versus a complete circuit. There are inquiries about the correctness of the magnetic field calculations and the interpretation of the circular path of integration.

Discussion Status

The discussion is ongoing, with various participants providing insights and suggestions regarding the application of Ampere's Law and the use of Biot-Savart Law. Some participants are questioning assumptions about the current distribution and the resulting magnetic fields, while others are exploring the relationship between the semicircular conductor and the complete circuit.

Contextual Notes

There are mentions of typographical errors in the equations and the need to clarify the radius of the circular path of integration. Participants are also considering the effects of additional wire segments on the magnetic field calculations.

  • #31
TSny said:
Yes, everything looks good. I was misinterpreting how you were using the word "equivalent". I thought you were implying that the semicircle current (alone) and the D loop produce the same result for the integral of Bnet around the circular path.

What if you replaced the semicircular current from A to B with a current of a different shape, such as shown in the attachment?

Are the points A and B along the axis of the integration circle?
 
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  • #32
If A and B are along the axis I would say the OP's a is correct but not b or c.

(I might as well benefit from this too!) :biggrin:
 
  • #33
rude man said:
If A and B are along the axis I would say the OP's a is correct but not b or c.

I wish TSny is a bit lenient in his marking :wink:. I somehow have the feeling that getting one answer correct should be enough to pass the test :-p.
 
  • #34
rude man said:
Are the points A and B along the axis of the integration circle?

Yes, I should have made that clear. A and B are still in the same location relative to the path of integration.
 
  • #35
Tanya Sharma said:
I wish TSny is a bit lenient in his marking :wink:. I somehow have the feeling that getting one answer correct should be enough to pass the test :-p.

Well, I'm retired. So, I refuse to do any more grading! :-p
But, if you were to use Tanya's suggested grading scheme, then you both passed. Tanya gets A+ on this one. (That is, her answers agree with mine, anyway.)
 
  • #36
Wow ! I can't believe I topped the class :-p

Have to say the Prof. is really cool :biggrin:.
 
  • #37
TSny said:
Well, I'm retired. So, I refuse to do any more grading! :-p
But, if you were to use Tanya's suggested grading scheme, then you both passed. Tanya gets A+ on this one. (That is, her answers agree with mine, anyway.)

Tanya's answers for b and c seem to have the wrong sign, otherwise I agree.

A downward current gives a positive B circulation as I understand it.
 
  • #38
Tanya Sharma said:
Wow ! I can't believe I topped the class :-p

Have to say the Prof. is really cool :biggrin:.

Congrats! And yes, we owe Dr. T. one - or actually several by now!
 

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