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The transformer shown in the figure consists of a long wire

The transformer shown in the figure consists of a long wire

The transformer shown in the figure consists of a long wire coincident with the z-axis carrying a current I = I0 cos ?t, coupling magnetic energy to a toroidal coil situated in the x–y plane and centered at the origin. The toroidal core uses iron material with relative permeability µr, around which 100 turns of a tightly wound coil serves to induce a voltage Vemf, as shown in the figure.


(a) Develop an expression for Vemf.
(b) Calculate Vemf for f = 60 Hz, µr = 4000, a =5 cm, b =6 cm, c =2 cm, and I0 = 50 A.

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