A pair of stationary and infinite long bent wires are placed in the xy-plane. The wires carrying currents of 10 A each as shown in figure. The segments L and M are along X-axis. The segments P and Q are parallel to y-axis, such that OS=OR=0.02m. The magnetic field induction at the origin O is

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$10^{- 3} T$

$10^{- 4} T$

$4 \times 10^{- 3} T$

$2 \times 10^{- 4} T$

answer is D.

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Detailed Solution

Total magnetic field induction at O is $B = B_{L R} + B_{R P} + B_{M S} + B_{S Q}$

$= 0 + \frac{μ_{0} i}{2 π r} + 0 + \frac{μ_{0} i}{2 π r} = \frac{μ_{0}}{2 π} \frac{2 i}{2} = \frac{2 \times 10^{- 7} \times 2 \times 10}{0.20} = 2 \times 10^{- 6} T$

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