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Three rings, each having equal y radius R, are placed mutually perpendicular to each other and each having its center at the origin of coordinate system. If current I is flowing through each ring, then the magnitude of the magnetic field at the common center is

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$(\sqrt{2} - 1) \frac{μ_{0} I}{2 R}$

zero

$\sqrt{3} \frac{μ_{0} I}{2 R}$

$(\sqrt{3} - \sqrt{2}) \frac{μ_{0} I}{2 R}$

answer is A.

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Detailed Solution

$\vec{B} = \frac{μ_{0} I}{2 R} (\pm \hat{i}) + \frac{μ_{0} I}{2 R} (\pm \hat{j}) + \frac{μ_{0} I}{2 R} (\pm \hat{k}) | \vec{B} | = \frac{μ_{0} I}{2 R} \sqrt{3}$

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