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Q.

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 I1 and I2 currents, respectively. Point P is lying at distance d from O along a direction perpendicular to the plane containing the wire. The magnetic field at the point P will be

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a

μ02πdI1I2

b

μ02πdI12+I22

c

μ02πdI1+I2

d

μ02πdI12+I221/2

answer is D.

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Detailed Solution

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The magnetic field at the point P, at a perpendicular distance d from O in a direction perpendicular to the plane containing A, B, C and D due to currents through AOB and COD are perpendicular to each other. Hence, 

B=B12+B221/2

=μ02πI1d2+μ02πI2d21/2

=μ02πdI12+I221/2

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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 I1 and I2 currents, respectively. Point P is lying at distance d from O along a direction perpendicular to the plane containing the wire. The magnetic field at the point P will be