Question

A current ' $I$ ' $A$ flows in a circular arc of radius ' $r$ ' subtending an angle ' $\theta$ ' as shown in the figure. Find the magnetic field at the center $O$ of the circle

• A. $\frac{{\mu }_{0}I\theta }{4\pi r}$
• B. $\frac{2{\mu }_{0}I\cdot \sin \theta }{4\pi r}$
• C. $\frac{2{\mu }_{o}I\cdot \sin \theta }{2r}$
• D. $\frac{2{\mu }_{o}I\cdot \sin \theta }{4r}$

Answer 1

Answer: (A)

Magnetic field at the centre due to current carrying circular loop is given as $B_C=\frac{{\mu }_{0}I}{2r}\dots$ (i)

Magnetic field due to current carrying circular arc making an angle theta at the centre, is given as
$B=\frac{\theta }{2\pi }\cdot B_C=\frac{\theta }{2\pi }\cdot \frac{{\mu }_{0}I}{2r}$ [From Eq. (i) ]
$B=\frac{{\mu }_{0}I\theta }{4\pi r}$