Two long parallel wires are placed perpendicular to the xy -plane, passing through the y -axis at points (0, a) and (0, -a) . They carry equal currents I in opposite directions. The magnitude of the net magnetic field at the point (a, 0) on the x -axis is:

Step-by-step solution

Let the wire at (0, a) carry current I out of the plane of the paper, and the wire at (0, -a) carry current I into the plane of the paper. The distance from each wire to the point (a, 0) is r = a^2 + a^2 = a 2 . The magnitude of the magnetic field produced by each wire at (a, 0) is: B₁ = B₂ = ₀ I 2 (a 2 ) Using the Right-Hand Grip Rule, the magnetic field vector B ₁ due to the wire at (0, a) points at an angle of 45^ above the positive x -axis. The magnetic field vector B ₂ due to the wire at (0, -a) points at an a