question_answer

The wire in the figure carries a current i and consists of a circular arc of radius R and central angle \[\frac{\pi }{2}\] rad, and two straight sections whose extensions intersect the center C of the arc. The magnetic field B that the current produces at C is

A)  \[\left| B \right|=\frac{{{\mu }_{0}}i}{8R}\] into the plane of the figure

B)  \[\left| B \right|=\frac{{{\mu }_{0}}i}{8R}\] out of the plane of the figure

C)  \[\left| B \right|=\frac{{{\mu }_{0}}i}{8\pi R}\] in  to the plane of the figure

D)  \[\left| B \right|=\frac{{{\mu }_{0}}i}{8\pi R}\] out of the plane of the figure

Correct Answer: C

Solution :

                 Magnetic field at C is                 \[B=\frac{1}{4}\] (due to whole circle)                 \[=\frac{1}{4}\left( \frac{{{\mu }_{0}}i}{2R} \right)=\frac{{{\mu }_{0}}i}{8R}\]