1. The problem statement, all variables and given/known data Not exactly a homework problem, but the actual working resembles it. Basically it is a standard calculation for the magnetic field between a set of Helmholtz coils, except with a rectangular loop instead of circular ie: two identical rectangular magnetic loops (dimensions L x W) carrying a current I in the same direction, placed symmetrically along a common axis, one on each side of the experimental area, separated by a distance d. I want to be able to calculate the total magnetic field due to the loops at ANY point in between them (off-axis magnetic field). I believe that for circular coils there is no analytical solution for this, but I *think* there should be for a rectangular loop. 2. Relevant equations Applying Biot-Savart Law 3. The attempt at a solution So at first we start with the same method for finding the on-axis field (which is relatively trivial) - find equations for the magnetic field caused by each loop separately and then sum them at a given point. We consider each loop as 4 segments of straight, finite wire (2 pairs of length L and W with the appropriate orientation), noting that each pair's current is going to flow in the opposite direction. Because of this fact, the on-axis field is easy because the magnetic field components off the axis for a line of wire cancels out with its opposite pair, so we just sum the 4 on-axis fields and we're done. We can't do this for the off-axis calculation, so I think we need to start looking at perpendicular lengths and angles to calculate the field due to the wire at any point. I can do this in two dimensions (ie: considering the wire to be along the y-axis, and the point we are finding the field at in the x-y plane), but start getting a bit confused in three dimensions when it comes to adding up the components from each side of the rectangular loop - unlike previously, each segment's field will point in a different direction without cancelling neatly. It occurs to me that the field's magnitude will be the same for a section of wire for the same perpendicular distance regardless of whether the point is neatly in the x-y plane or not, but I get a bit confused combining the different directions with other segments of wires. Any advice or suggestions would be greatly appreciated!