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?

Explanation

(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`