A long straight wire carrying a current of 100A coincides with the principal axi

Question

A long straight wire carrying a current of 100A coincides with the principal axis of symmetry of a 200 - turn rectangular toroid of inner and outer radii a = 4cm and b = 6cm. thickness t = 3cm, core material with mu r = 250, respectively. No current flows in the toroid. Find the total magnetic flux linking the toroid due to the current in the long, straight wire. Consider an air - core rectangular toroid with its dimensions given by a = 3.8mm. b = 6.4mm. and t = 4.8mm. respectively, ( a ) Find the total number of turns to be wound on this core such that its total inductance is around 1mH. ( b ) Repeat part ( a ) for a powdered nickel - iron core with nr 200 and the same dimensions.

Explanation / Answer

1) I = 100 A, N = 200 turns, a = 4 cm, b = 6 cm, t = 3 cm, r = 250,

B = 0rI/(2r)

flux = Nab B*t*dr = 0rNIt*ln(b/a)/(2) = 0.0122 Wb

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