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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?


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

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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

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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