The magnetic field due to a current carrying square loop of side a at a point located symmetrically at a distance of $a/2$ from its centre (as shown is)
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$(A C)^{2}=(A B)^{2}+(B C)^{2}$
$\Rightarrow A C=\frac{\sqrt{3}}{2}$
$\sin \theta=\frac{1}{\sqrt{3}}$
$\mu \times \frac{\mu 0}{\mu \pi} \frac{I}{a} \times \frac{2}{\sqrt{3}}$
$=\frac{2 \mu oi}{\sqrt{3} \pi a}$
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