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Find the magnitude of the magnetic induction B of a magnetic field generated by a system of thin conductors along which a current i is flowing at a point A (O, R, O), that is the centre of a circular conductor of radius R. The ring is in yz plane.

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$B = \frac{μ_{0} i}{2 π R} \sqrt{(2 π^{2} - 2 π + 1)}$

$B = \frac{μ_{0} i}{4 π R} \sqrt{(2 π^{2} - 2 π + 1)}$

None of these

$B = \frac{μ_{0} i}{4 π R} \sqrt{2 (2 π^{2} - 2 π + 1)}$

answer is B.

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Detailed Solution

${\vec{B}}_{A} = \frac{μ_{0} i}{4 π R} \hat{k} + \frac{μ_{0} I}{2 R} \hat{i} - \frac{μ_{0} I}{4 π R} \hat{i} B_{A} = \frac{μ_{0} I}{4 π R} \sqrt{(2 π - 1)^{2} + (1)^{2}} = \frac{μ_{0} I}{4 π R} \sqrt{2 (2 π^{2} - 2 π + 1)}$

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