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Q. The wire shown is figure carries a current of $32 A$. If $r=3.14\, cm$, the magnetic field at point $P$ will bePhysics Question Image

AIIMSAIIMS 2013

Solution:

Magnetic field due to a complete circular wire loop carrying a current $I$ at the centre is $\frac{\mu_{0} I}{2r}$
Here, the straight portions of the wire do not contribute because the point $P$ is along them. The field at $P$ is due to $\frac{3}{4}$ th of the loop of radius $r$. Thus
$B =\frac{3}{4}\left(\frac{\mu_{0} I}{2 r}\right) $
$=\frac{3}{4} \times \frac{4 \pi \times 10^{-7} \times 32}{2 \times 314 \times 10^{-7}}$
$=4.8 \times 10^{-6} T$