Question

In figure,the curved part represents arc of a circle of radius x.If it carries a current $I$,then the magnetic field at the point O is :

• A. $\frac{{\mu }_{o}I\varphi }{2\pi x}$
• B. $\frac{{\mu }_{o}I\varphi }{4\pi x}$
• C. $\frac{{\mu }_{o}I\varphi }{2x}$
• D. $\frac{{\mu }_{o}I\varphi }{4x}$

Answer 1

The correct option is B $\frac{{\mu }_{o}I\varphi }{4\pi x}$

Magnetic field due the straight portions is zero.It is only due to arc of circle
$\therefore B=\frac{\varphi }{2\pi }\left(\frac{{\mu }_{o}I}{2x}\right)$ (Radius =x)
$=\frac{{\mu }_{o}I\varphi }{4\pi x}$