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According to Gauss's law of magnetism, the total magnetic flux through a closed surface is zero. But during induction, we study that the magnetic field lines passing through a coil change, as does flux given by $\Phi = LI$. But even if they change, the net lines coming in= net lines going out. So, flux should be zero?

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  • $\begingroup$ What do mean with: "net lines coming in= net lines going out"? $\endgroup$ Jun 9, 2017 at 11:03
  • $\begingroup$ I mean that the total number of magnetic field lines are equal to the total number of magnetic field lines going out $\endgroup$
    – OFFplanet
    Jun 9, 2017 at 11:05
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    $\begingroup$ For coil magnetic flux, the surface the magnetic field lines pierce is not closed. $\endgroup$ Jun 9, 2017 at 12:07

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Gauss's law of magnetism does not give us a tool to "measure" flux. As you said it just says that the total magnetic flux through a closed surface is zero.

If we take a coil with changing magnetic field and imagine a sphere around it, Gauss law tell's us that the total flux through the surface of the sphere is zero, what helps us in no way.

Field lines are just a tool to represent intensity of the magnetic field with drawing (less) denser lines, and representing the direction the field at a given position. You can't argue with the "amount" of field lines.

But as you stated magnetic flux through a coil is given by $$\Phi = LI$$

So flux is not zero for $I, L \ne 0$.

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According to Gauss' Law, the "net" magnetic flux is zero for a closed surface because magnetic monopoles don't exist but by writing $\Phi=LI$, we measure the outflux/influx produced by the single pole but though the "net" flux here also is zero.

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