A current 'I' flows in anticlockwise direction in a circular arc of a wire having…
A current 'I' flows in anticlockwise direction in a circular arc of a wire having $\left(\frac{3}{4}\right)^{\text {th }}$ of circumference of a circle of radius R. The magnetic field ' $B$ ' at the centre of circle is ( $\mu_0=$ permeability of free space)
$\frac{\mu_0 \mathrm{I}}{3 \mathrm{R}}$ in upward direction
$\frac{\mu_0 \mathrm{I}}{2 \mathrm{R}}$ in downward direction
$\frac{3 \mu_0 \mathrm{I}}{8 \mathrm{R}}$ in downward direction
$\frac{3 \mu_0 \mathrm{I}}{8 \mathrm{R}}$ in upward direction
Solution
Magnetic field due to $\theta$ angle $B=\frac{\theta}{2 \pi} \times \frac{\mu_0 I}{2 R}$
$\begin{aligned}
& \theta=\frac{3}{4} \times 2 \pi r=\frac{3}{2} \pi \\
& B=\frac{3 \pi}{4 \pi} \times \frac{\mu_0 I}{2 R}=\frac{3 \mu_0 I}{8 R}
\end{aligned}$