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Toroid with Air Gap magnetostatics problem
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[QUOTE="Charles Link, post: 6036928, member: 583509"] You need another form of Ampere's law which is ## \oint H \cdot dl=NI ##. The ## H ## is not continuous though in this problem, while the ## B ## is assumed to be continuous. ## H ## will take on a different value in the air gap=call that ## H_1(r) ##, and ## H_2(r) ## will be the value in the iron. Expressing the continuity of ## B ## at a distance ## r ## from the center: ##B(r)=\mu_o H_1(r)=\mu_o (H_2(r)+M) ##. ## \\ ## Next, write ## \oint H(r) \cdot dl =NI ## in terms of ## H_1(r) ## and ##H_2(r) ##, and then with just ##H_2(r) ## by substituting in for ##H_1(r) ##. With these hints, you should be able to complete it, by solving for ## H_2(r) ##. ## \\## Note: The standard form of Ampere's law is ## \oint B \cdot dl=\mu_o I_{total} ## where ## I_{total}=I_{conductors}+I_{m} ##, where ## I_{m} ## is from magnetic currents and magnetic surface currents. The ## I_m ## requires extra computation, and it is far simpler to just use ## \oint H \cdot dl=I_{conductors}=NI ##. [/QUOTE]
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Toroid with Air Gap magnetostatics problem
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