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Q. In the figure shown, the magnetic field induction as the point $O$ will bePhysics Question Image

VITEEEVITEEE 2012

Solution:

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
image
length while at the centre of a semicircular coil is $\frac{\mu_{0} \pi i}{4 \pi r}$
$\therefore B=B_{a}+B_{b}+B_{c}$
$=\frac{\mu_{0}}{4 \pi} \frac{i}{r} \cdot+\frac{\mu_{0}}{4 \pi} \frac{\pi i}{r} \cdot+\frac{\mu_{0}}{4 \pi} \frac{i}{r}$
$=\frac{\mu_{0}}{4 \pi} \frac{i}{r}(\pi+2)$ out of the phase