Two identical long conducting wires AOB and COD are placed at right… | NEET 2014 (AIPMT)

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Magnetic Field of Straight Wires

Two identical long conducting wires $AOB$ and $COD$ are placed at right angle to each other, with one above other such that $O$ is their common point for the two. The wires carry $I$ 1 and $I$ 2 currents, respectively. Point $P$ is lying at distance f from $O$ along a direction perpendicular to the plane containing the wires. The magnetic field at the point $P$ will be

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Answer: (d)

P is at perpendicular distance $d$ from both long wires (P lies above their crossing point O).
$B_1 = \frac{\mu_0 I_1}{2\pi d}$ , $B_2 = \frac{\mu_0 I_2}{2\pi d}$ ; since the wires are perpendicular, $B_1 \perp B_2$ .
$B = \sqrt{B_1^2 + B_2^2} = \frac{\mu_0}{2\pi d}\left(I_1^2 + I_2^2\right)^{1/2}$
So the answer is (d).

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