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I needed some help with a problem from the Griffiths Book on EM. It's problem number 6.10 if anyone has the book. Here is the problem and I have attached a crude drawing using MSPaint.

An iron rod of lengthLand square cross section (sidea), is given a uniform longitudinal magnetizationM, and then bent around into a circle with a narrow gap (widthw). Find the magnetic field at the center of the gap, assumingw<<a<<L. [Hint: treat it as the superposition of a complete torus plus a square loop with reversed current.]

The field inside a toroid is: [tex]B= \frac{\mu_0 NI}{2\pi s}[/tex]. The hint would lead me to believe that I can takeNI -> M. The field at the center of the gap due to a loop of current in the opposite direction would be:[tex]B=-\frac{2\sqrt{2}\mu_0 I}{\pi a} [/tex].

This means the answer would be:

[tex]B=\frac{\mu_0 NI}{L} - \frac{2\sqrt{2}\mu_0 I}{\pi a}[/tex].

However I don't see how to resolve the current(I) in this problem. Is there a way to relateMandIor am I going about this problem in the completely wrong direction.

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# Homework Help: Magnetized Toroid

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