Find the magnetic field at $P$ due to the arrangement shown
Diffcult
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$\mathrm{B}=\overrightarrow{\mathrm{B}}_{1}+\overrightarrow{\mathrm{B}}_{2}$
$\mathrm{B}=\frac{\mu_{0} \mathrm{I}}{4 \pi \frac{\mathrm{d}}{\sqrt{2}}}\left(-\sin \frac{\pi}{4}+\sin \frac{\pi}{2}\right) \times 2 \otimes$
$\mathrm{B}=\frac{\mu_{0} \mathrm{I}}{2 \pi \frac{\mathrm{d}}{\sqrt{2}}}\left(1-\frac{1}{\sqrt{2}}\right) \otimes$
$\mathrm{B}=\frac{\sqrt{2} \mu_{0} \mathrm{I}}{2 \pi \mathrm{d}}\left(\frac{\sqrt{2}-1}{\sqrt{2}}\right) \otimes$
$\therefore \mathrm{B}=\frac{\mu_{0} \mathrm{I}}{2 \pi \mathrm{d}}(\sqrt{2}-1) \otimes$
$\mathrm{B}=\frac{\mu_{0} \mathrm{i}}{\sqrt{2} \pi \mathrm{d}}\left(1-\frac{1}{\sqrt{2}}\right) \otimes$
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