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. $\frac{2 \mu_{o} I \cdot \sin \theta}{2 r}$
• D. $\frac{2 \mu_{o} I \cdot \sin \theta}{4 r}$

Answer 1

Answer: (A)

Magnetic field at the centre due to current carrying circular loop is given as $B_{C}=\frac{\mu_{0} I}{2 r} \ldots$ (i)

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