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(D) The magnetic field due to an infinite wire at a distance $r$ is given by $B = \frac{\mu_0 I}{2 \pi r}$.At point $M$,which is at a distance $a$ fro

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$\frac{\mu_0 I}{\sqrt{2} \pi a}$

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(D) The magnetic field due to an infinite wire at a distance $r$ is given by $B = \frac{\mu_0 I}{2 \pi r}$.At point $M$,which is at a distance $a$ from both wires,the magnitude of the magnetic field due to each wire is $B_1 = B_2 = \frac{\mu_0 I}{2 \pi a}$.The magnetic field due to the vertical wire (carrying current upwards) at point $M$ is directed into the plane of the paper (using the right-hand thumb rule).The magnetic field due to the wire carrying current out of the plane (represented by the dot) at point $M$ is directed downwards.Since these two magnetic field vectors are perpendicular to each other,the resultant magnetic field $B_M$ is given by:$B_M = \sqrt{B_1^2 + B_2^2} = \sqrt{\left(\frac{\mu_0 I}{2 \pi a}\right)^2 + \left(\frac{\mu_0 I}{2 \pi a}\right)^2}$$B_M = \sqrt{2 \left(\frac{\mu_0 I}{2 \pi a}\right)^2} = \sqrt{2} \cdot \frac{\mu_0 I}{2 \pi a} = \frac{\mu_0 I}{\sqrt{2} \pi a}$.

Two infinite length wires are placed as shown in the figure. Find the magnitude of the magnetic field at point $M$,which is the midpoint of the line joining the two wires.

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