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Two straight long conductors AOB and COD are perpendicular to each other and carrying currents $I_{1} and I_{2}$ . The magnitude of the magnetic induction at a point P at a distance d from the point O in a direction perpendicular to the plane ABCD is :

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$\frac{μ_{0}}{4 πd} (I_{1} - I_{2})$

$\frac{μ_{0}}{2 πd} (I_{1} + I_{2})$

$\frac{μ_{0}}{2 πd} \sqrt{(I_{1}^{2} + I_{2}^{2})}$

$\frac{μ_{0}}{2 πd} (\frac{I_{1} I_{2}}{I_{1} + I_{2}})$

answer is C.

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Detailed Solution

$B_{1} = \frac{μ_{o} i_{1}}{2 π d} and B_{2} = \frac{μ_{o} i_{2}}{2 π d}$

$B = \sqrt{B_{1}^{2} + B_{2}^{2}}$

$= \frac{μ_{o}}{2 π d} \sqrt{i_{1}^{2} + i_{2}^{2}}$

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