Consider (in 3 dimensions) a regular square lattice of wires spaced 1 cm apart, each carrying a current of 0.5 A, with the direction of the current alternating in adjacent wires. Let the wires all run in the z direction, with the ones at (0,0) cm, (0,2) cm, (2,0) cm, (2,2) cm and (1,1) cm carry current into the page, with (0,1) cm, (1,0) cm, etc. carrying current out. What does the magnetic field between adjacent wires look like? While a completely accurate answer would require some infinite series or extreme cleverness, just try to draw a rough map of where the field point over the square from the origin to (2,2) cm, with the understanding that each wire dominates its local neighborhood. Then calculate the field at (0.5, 0.5) cm.
