Lets say there is a single loop of wire. Is the B field at exactly of the plane of the loop going to all be perpendicular and of constant magnitude, at exactly the plane of the loop. I know this is true for the center. Doesnt it also hold for points off center of the loops axis, as long as we stay on the plane of the loop and dont move away from it. Also, wont the magnitude of B be the same at all points on the plane inside the loop as well? I thought of this as follows. If we do the right hand rule at all points on the plane, then the B field is going to be perpendicular to the loop, becuase theres nothing that will make it angle from being perpendicular. The current I is constant so we can factor that out. So any point off center will be the sum of all the R's times the I around the loop. But that always works out to the area of the circle times I. So the B field should be uniform, and constant, when looking at any point contained in the plane of the loop.