Three rings, each having equal radius $R,$ are placed mutually perpendicular to each other and each having its centre at the origin of co-ordinate system. If current $I$ is flowing thriugh each ring then the magnitude of the magnetic field at the common centre is
Diffcult
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$\vec{B}=B_{x} \hat{i}+B_{y} \hat{j}+B_{z} \hat{k}$
$B=\sqrt{B_{x}^{2}+B_{y}^{2}+B_{z}^{2}}$
since $B_{x}=B_{y}=B_{z} s o B=\sqrt{3} B_{0}$
$B=\sqrt{3} . \frac{\mu_{0}}{4 \pi} \frac{2 \pi I}{R}=\sqrt{3} \frac{\mu_{0} I}{2 R}$
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