Question

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

Answer 1

Answer: (A)

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} $