Question

A wire carrying current $i$ has the configuration as shown in the figure. Two semi-infinite straight sections, each tangent to the same circle, are connected by a circular arc, of angle $\theta ,$ along the circumference of the circle, with all sections lying in the same plane. What must $\theta (\text{in rad) be in order for}B$ to be zero at the center of circle is

Answer 1

From directions of current, the field due to straight wires is outwards and field due to the arc is inward.

Therefore in order to the field at O to be zero,

$\frac{{\mu }_{0}I}{4\pi R}+\frac{{\mu }_{0}I}{4\pi R}=\frac{{\mu }_{0}I}{2R}\left(\frac{\theta }{2\pi }\right)$

$\Rightarrow \theta =2rad$