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 $I_{1} a n d I_{2}$ currents, respectively. Point P is lying at distance d 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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$\frac{μ_{0}}{2 π d} {(I_{1}^{2} + I_{2}^{2})}^{1 / 2}$

$\frac{μ_{0}}{2 π d} (I_{1} + I_{2})$

$\frac{μ_{0}}{2 π d} (\frac{I_{1}}{I_{2}})$

$\frac{μ_{0}}{2 π d} (I_{1}^{2} - I_{2}^{2})$

answer is D.

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Detailed Solution

Two conductors AOB and COD are carrying current i1 and i2, respectively. Magnetic field at point P needs to be found out.
Question Image
Magnetic field due to AOB is $\frac{μ_{0} I_{i}}{2 π d}$ along the direction parallel to OD, and magnetic field due to COD is $\frac{μ_{0} I_{2}}{2 π d}$ along the direction parallel to OB.
As they are perpendicular, resultant fi eld is $\frac{μ_{0}}{2 π d} \sqrt{l_{1}^{2} + I_{2}^{2}} .$