Two infinitely long, thin, insulated, straight wires lie in the x-y plane along the x- and y-axes respectively. Each wire carries a current I, respectively in the positive x-direction and positive y-direction. The magnetic field will be zero at all points on the straight line:

If a wire carries current along positive x-axis, then the magnetic field due to it along the line y = x in first quadrant is upwards. If a wire carries current along positive y-axis, then the magnetic field due to it along the line y = x in first quadrant is downwards. Along the line y = x, above two values of magnetic field are equal in magnitude but opposite in direction and thus, their resultant is zero.