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I have seen in the book that the answer would be same as that of an infinitely long wire $\frac{\mu_0 I}{2\pi a }$ how can we prove that though? I'm really not convinced and have tried to prove it using Ampere's Law & Biot-Savart without any success.

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  • $\begingroup$ Note: I have tried similar proof as that done to Toroid Case I reached something close but not exactly the same $\endgroup$ May 20, 2018 at 22:48

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If your drawing is taken from the book, it is possible that you've just misinterpreted the question.

In the question, you are referring to a coil as if the magnetic field was produced by the current in the coil. On the drawing, however, the coil is producing EMF, but the current is flowing in a wire going up along the z axis and, by its look, it might be flowing in an infinitely long wire.

So, if the inner radius of the core is greater than a, the magnetic field at distance a from the wire would be exactly as stated. If the inner radius of the core is a little less than a, the field of interest would be inside the core and, therefore, the answer would be: $B=\frac {\mu_0 \mu_r I} {2\pi a}$.

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  • $\begingroup$ I used the figure from the book, however, my question is if we can in general (ignoring the wire in the middle) find the magnetic field of a coil wrapped around a core in same manner as toroid case $\endgroup$ May 21, 2018 at 0:10
  • $\begingroup$ Sure, but the formula will be a bit different. You can check out this Hyperphysics page: hyperphysics.phy-astr.gsu.edu/hbase/magnetic/toroid.html $\endgroup$
    – V.F.
    May 21, 2018 at 0:20

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