The transformer shown in Fig. consists of a long wire coincident with the z-axis carrying a current I = Io cos ωt, 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 permeabilit μr, around which 100 turns of a tightly wound coil serves to induce a voltage Vemf shown in the figure.
Figure
Figure : Problem. |
(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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