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Constant Magnetic Field, Magnetics

Problem 3.223

Find the magnetic induction of the field at the point OO of a loop with current II, whose shape is illustrated (a) in Fig. 3.60a3.60 a, the radii aa and bb, as well as the angle φ\varphi are known; (b) in Fig. 3.60b3.60 b, the radius aa and the side bb are known.

Reveal Answer
(a) B=μ0I4π(2π−φa+φb)B=\frac{\mu_{0} I}{4 \pi}\left(\frac{2 \pi-\varphi}{a}+\frac{\varphi}{b}\right) (b) B=μ0I4π(3π4a+2b)B=\frac{\mu_{0} I}{4 \pi}\left(\frac{3 \pi}{4 a}+\frac{\sqrt{2}}{b}\right).
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