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A thin iron ring with mean diameter `d = 50 cm` supports a winding consisting of `N = 800` turns carrying current `I = 3.0A`. The ring has a cross-cut of width `b = 2.0 mm`. Neglecting the scattering of the magnetic flux at the gap edges, and using the plot shown in FIg. find the permeabitliy of iron under these conditions. |
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Answer» From the theorem on circulatiaon of vector `vec(H)` `H pi d + (B b)/(mu_(0)) = N I` or, `B = (mu_(0) N I)/(b) - (mu_(0) pi d)/(b) H = (1.51 - 0.987) H`, where `B` is the Tesla and `H` in `Ka//m`. Besides, `B` and `H` are interralates as in the fig of the text thus we have to solve for `B, H` graphically by simulancously drawing the two curves (the hysterists curve and the straight line, graph line, given above) and find the point of intersection. It is at `H = 0.26 kA//m, B = 1.25 T` Then, `mu = (B)/(mu_(0) H) = 4000` |
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