magnetism mamamiya

A thin ring made of a magnetic material of permeability has a mean diameter d and supports a winding of N turns. The crosssectional area of the ring is equal to S. The ring has a cross-cut of width b such that b << d. The winding carries a certain current I. Neglecting the leakage of flux at the gap edges, answer the following.

Ques.
1]The magnetic flux density B in the gap is
2]Inductance of the system L is
3]Ratio of magnetic energy in the gap to that in the ring of magnetic material is

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