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.

Explanation

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`