Two long, straight wires, one above the other, are separated by a distance 2a and are parallel to the x-axis. Let the y-axis be in the plane of the wires in the direction form the lower wire to the upper wire. Each wire carries current I in the +x-direction. What are the magnitude and direction of the net magnetic field of the two wires at a point in the plane of wires: (a) midway between them? (b) at a distance a above the upper wire? (c) at a distance a below the lower wire?

Two long, straight wires, one above the other, are separated by a dist

1.	Two long, straight wires, one above the other, are separated by a distance 2a and are parallel to the x-axis. Let the y-axis be in the plane of the wires in the direction form the lower wire to the upper wire. Each wire carries current I in the +x-direction. What are the magnitude and direction of the net magnetic field of the two wires at a point in the plane of wires: (a) midway between them? (b) at a distance a above the upper wire? (c) at a distance a below the lower wire?
Answer» (a) At the point exactly midway between the wires, the two magnetic fields are in opposite directions and cancel. (b) At a distance a above the top wire, the magnetic fields are in the same direction and add up `vecB=(mu_0I)/(2pir_1)hatk+(mu_0I)/(2pir_2)hatk=(mu_0I)/(2pia)hatk+(mu_0I)/(2pi(3a))hatk=(2mu_0I)/(3pia)hatk` (c) At a distance a below the lower wire, magnitude magnetic field is same as in part (b) but is in the opposite direction `vecB=-(2mu_0I)/(3pia) hatk`

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