Question

a) The transformer shown in Figure B2.1 consists of an infinitely long wire along the z-axis carrying a current I-cos ot, which couples to an iron toroid centred on the origin (0, 0, 0) and lying in the x-y plane. The iron toroid has a 100 turns coil tightly wound around it which induces a voltage Vemf as shown in Figure B2.1 The permeability of the iron toroid is r, and it has an outer radius of b, inner radius of a, and thickness of c. (i) Derive an expression for Vemj hint: start by considering the magnetic flux ? through the coil. (ii) Calculate Veny for 50 Hz, m=4000, a=5 cm, b= 6 cm, c=l cm, and o 40 A (3) 1 emf Cl Iron core with ur Figure B2.1

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a) Dexiv« expi«ssicn [ol Lets take hovizonbal Crass sectiam j e | B.dl Да! longh the i ajl3-b 2TT a. 10m dt 2TT dt 2TT RTmї) Vent r I. 832 sin (Oort) v.

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