ch30-p060 - 60. (a) Our notation is as follows: h is the...

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60. (a) Our notation is as follows: h is the height of the toroid, a its inner radius, and b its outer radius. Since it has a square cross section, h = b – a = 0.12 m – 0.10 m = 0.02 m. We derive the flux using Eq. 29-24 and the self-inductance using Eq. 30-33: Φ B a b a b BdA Ni r hdr Nih b a == F H G I K J = F H G I K J z z µµ 00 22 ππ ln and 2 0 ln 2 B Nh N b L ia µ Φ ⎛⎞ ⎜⎟ π ⎝⎠ . Now, since the inner circumference of the toroid is l = 2 π a = 2 π (10 cm) 62.8 cm, the number of turns of the toroid is roughly N 62.8 cm/1.0 mm = 628. Thus
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