Question

In the figure shown, the magnetic field induction at the point $O$ will be

• A. $\frac{\mu_{0} {i}}{2 \pi r}$
• B. $\left(\frac{\mu_{0}}{4 \pi}\right)\left(\frac{i}{r}\right)(\pi+2)$
• C. $\left(\frac{\mu_{0}}{4 \pi}\right)\left(\frac{i}{r}\right)(\pi+1)$
• D. $\frac{\mu_{0}}{4 \pi} \frac{i}{r}(\pi-2)$

Answer 1

Answer: (B)

Field due to a straight wire of infinite length is $\frac{\mu_{0}^{i}}{4 \pi r}$ if the point is on a line perpendicular to its length while at the centre of a semicircular coil is $\frac{\mu_{0} \pi i}{4 \pi r}$.

$\therefore B=B_{a}+B_{b}+B_{c}$
$=\frac{\mu_{0}}{4 \pi} \frac{i}{r}+\frac{\mu_{0}}{4 \pi} \frac{\pi i}{r}+\frac{\mu_{0}}{4 \pi-} \frac{i}{x}$
$=\frac{\mu_{0}}{4 \pi} \frac{i}{r}(\pi+2)$ out of the page