Three infinite wires are arranged in space in three dimensions.(along $x, y$ and $z$ axis) as shown. Each wire carries current $i$ . Find magnetic field at $A$
Diffcult
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Magnetic field at $A$ due to
Due to $(1)$ $\mathrm{B}_{1}=\frac{\mu_{0} \mathrm{i}}{2 \pi \mathrm{r}}(-\mathrm{k})$
Due to $(2)$ $\mathrm{B}_{2}=\frac{\mu_{0} \mathrm{i}}{2 \pi r}(-\mathrm{k})$
Due to $(3)$ ${\mathrm{B}_{3}}=\frac{\mu_{0} \mathrm{i}}{2 \sqrt{2} \pi \mathrm{r}}(\cos \theta \mathrm{i}+\sin \theta \mathrm{j})$
$\frac{\mu_{0} i}{4 \pi r} \hat{i}+\frac{\mu_{0} i}{4 \pi r} \hat{j}$
$\mathrm{B}=\mathrm{B}_{1}+\mathrm{B}_{2}+\mathrm{B}_{3}=\frac{\mu_{0} \mathrm{i}}{4 \pi \mathrm{r}} \mathrm{i}+\frac{\mu_{0} \mathrm{i}}{4 \pi \mathrm{r}} \mathrm{j}-\frac{\mu_{0} \mathrm{i}}{\pi \mathrm{r}} \hat{\mathrm{k}}$
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