A wire carrying current $I$ has the shape as shown in adjoining figure.Linear parts of the wire are very long and parallel to $X-$axis while semicircular portion of radius $R$ is lying in $Y-Z$ plane. Magnetic field at point $O$ is
AIPMT 2015, Diffcult
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Given situation is shown in the figure.
Parallel wires $1$ and $3$ are semi-infinite, so magnetic field at $O$ due to them
$\vec{B}_{1}=\vec{B}_{3}=-\frac{\mu_{0} I}{4 \pi R} \hat{k}$
Magnetic field at $O$ due to semi-circular $arc$ in
$YZ-$plane is given by $\vec{B}_{2}=-\frac{\mu_{0} I}{4 R} \hat{i}$
Net magnetic field at point $O$ is given by
${\vec{B}=\vec{B}_{1}+\vec{B}_{2}+\vec{B}_{3}}$
${=-\frac{\mu_{0} I}{4 \pi R} \hat{k}-\frac{\mu_{0} I}{4 R} \hat{i}-\frac{\mu_{0} I}{4 \pi R} \hat{k}}$
${=-\frac{\mu_{0} I}{4 \pi R}(\pi \hat{i}+2 \hat{k})}$
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