Question

The magnetic induction at centre $O$ due to the arrangement shown in fig-

• A. $\frac{{\mu }_{0}i}{4\pi r}(1+\pi )$
• B. $\frac{{\mu }_{0}i}{4\pi r}$
• C. $\frac{{\mu }_{0}i}{4\pi r}(1-\pi )$
• D. $\frac{{\mu }_{0}i}{r}$

Answer 1

The correct option is A $\frac{{\mu }_{0}i}{4\pi r}(1+\pi )$

REF.Image.

The diagram will be

(1) magnetic field due to PQ will be :-

$B_{PQ}=\frac{{\mu }_0}{4\pi }\frac{i}{r}$ above the plane of paper

(ii) magnetic field due to QR will be:-

$B_{QR}=\frac{{\mu }_0}{4\pi }\frac{\pi i}{r}$ above the plane of paper.

(iii) magnetic field due to OR will be :-

$B_{OR}=0$ because it crosses the point O.

$\because$ All the magnetic field intensities are in same direction :-

$B_{net}=B_{PQ}+B_{QR}+B_{OR}$

$B_{net}=\frac{{\mu }_0}{4\pi }\frac{i}{r}(1+\pi )$