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buhthestuh
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Hello,
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 length L and square cross section (side a), is given a uniform longitudinal magnetization M, and then bent around into a circle with a narrow gap (width w). Find the magnetic field at the center of the gap, assuming w << 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 take NI -> 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 relate M and I or am I going about this problem in the completely wrong direction.
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 length L and square cross section (side a), is given a uniform longitudinal magnetization M, and then bent around into a circle with a narrow gap (width w). Find the magnetic field at the center of the gap, assuming w << 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 take NI -> 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 relate M and I or am I going about this problem in the completely wrong direction.
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