All Problems

Constant Magnetic Field, Magnetics

Problem 3.223

Find the magnetic induction of the field at the point \(O\) of a loop with current \(I\), whose shape is illustrated (a) in Fig. \(3.60 a\), the radii \(a\) and \(b\), as well as the angle \(\varphi\) are known; (b) in Fig. \(3.60 b\), the radius \(a\) and the side \(b\) are known.

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