# Finding Magnetic Field of Coil (Wound around a core)

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.

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

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: $B=\frac {\mu_0 \mu_r I} {2\pi a}$.