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JD_PM
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Homework Statement
Imagine an infinite straight wire pointing at you (thus, the magnetic field curls counterclockwise from your perspective). Such a magnetic field equals to:
$$B = \frac{\mu I}{2 \pi s} \hat{\phi}$$
I want to calculate the line integral of ##B## around the circular path of radius ##s##
Homework Equations
The Attempt at a Solution
I know the solution:
But I have been thinking on how could we prove that it does not have to be circle. The line integral over the closed path should always yield the perimeter of a circle for the answer not to change. However, this seems contradictory; I actually want to proof that it does not depend on the path.
What am I missing here?
Thanks
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