Question

A wire is bent in the form of a circular arc of radius ‘r’ with a straight portion AB. If the current in the wire is I, find magnetic induction at O.

• A. $\frac{{\mu }_{0}i}{2\pi r}\left(tan\varphi \right)$
• B. $\frac{{\mu }_{0}i}{2\pi r}(\pi -\varphi )$
• C. $\frac{{\mu }_{0}i}{2\pi r}(\pi -\varphi +tan\varphi )$
• D. $\frac{{\mu }_{0}i}{2\pi r}(\pi -tan\varphi )$

Answer 1

The correct option is C $\frac{{\mu }_{0}i}{2\pi r}(\pi -\varphi +tan\varphi )$

$B=B_1+B_2=\frac{{\mu }_{0}i}{4\pi r}[2\pi -2\varphi ]+\frac{{\mu }_{0}i}{4\pi a}2sin\varphi =\frac{{\mu }_{0}i}{2\pi r}[\pi -\varphi +\frac{sin\varphi }{cos\varphi }],here[cos\varphi =\frac{a}{r}a=rcos\varphi ]B=\frac{{\mu }_{0}i}{2\pi r}[\pi -\varphi +tan\varphi ]$