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This question already has an answer here:

Imagine a wire with current I flowing through it. If we take a closed loop that doesnt contain the I the line integral will be zero. Does this means magnetic field is zero ? Also does Ampere law calculating the total magnetic field or only the sum of magnetic fields from the currents that are enclosed in the loop?

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marked as duplicate by Aaron Stevens, ZeroTheHero, John Rennie electromagnetism Feb 10 at 7:03

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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    $\begingroup$ @AaronStevens nice catch; your memory is better than mine, or I’ve been here too long, or both. $\endgroup$ – ZeroTheHero Feb 10 at 1:33
  • $\begingroup$ @ZeroTheHero Nah I just searched to see if there was a similar question. I can't remember things either :) $\endgroup$ – Aaron Stevens Feb 10 at 3:03
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of course not. Unless you can argue that the magnetic field is constant over the loop so that $\oint \vec B\cdot d\vec \ell= \vert\vec B \vert \oint d\ell$ you cannot deduce anything about $\vec B$.

In the same way if a Gaussian surface encloses no charge it does not mean the field is 0 unless the magnitude of $\vec E$ is constant over the surface.

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