The magnetic field at the midpoint on the axis of a current loop is given by $B=\frac{{\mu }_{0}I{R}^2}{2{(R^2+z^2)}^{3/2}}$. At the midpoint between two loops, the net field is the vector sum of the fields from each loop. The direction of the current determines the field's direction (right-hand rule).

In arrangement 1, the fields from the two loops oppose and partially cancel. In arrangement 2, the fields add together. In arrangement 3, the fields also oppose but are closer together than in 1, leading to a stronger cancellation. Therefore, the magnitudes from minimum to maximum are: 3 (strongest cancellation), 1 (partial cancellation), 2 (addition).

Final Answer: 3, 1, 2