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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=3.0 A. 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 permeability of iron under these conditions.

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#### From the theorem on circulation of vector →H,Hπd+Bbμ0=NI or, B=μ0NIb−μ0πdbH=(1.51−0.987)H,Where B is in Tesla and H in kA/m. Besides, B and H are interrelated as in the figure shown below of the text. Thus we have to solve for B, H graphically by simultaneously drawing the two curves (the hysterisis curve and the straight line, given above) and find the point of intersection. It is atH≈0.26kA/m, B=1.25TThen μ=Bμ0H≈4000.

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Q1
A thin iron ring with mean diameter d=50 cm supports a winding consisting of N=800 turns carrying current I=3.0 A. 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 permeability of iron under these conditions.

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Q2
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