To determine the total magnetic field produced by two coils, we need to know the individual magnetic fields produced by each coil and then add them together vectorially. Let's assume that the two coils have the same radius Fl, the same number of turns N, and are separated by a distance d. The magnetic field produced by a single coil at a distance r from the center of the coil is given by: Blr) = (u. ' N * | * R2) / (2 ' (R2 + raw/2') where [1D is the permeability of free space. | is the current in the coil, and Fl is the radius of the coil. Using the principle of superposition. we can find the total magnetic field produced by both coils at a point P in space by adding the magnetic fields produced by each coil at that point: Btotal(P) = B103) 4' 320)) where B,(P) and BZ(P) are the magnetic elds produced by each coil at point P. Since the two coils are symmetrically arranged with respect to the y-axis, we can simplify the expression by considering only the y-component of the magnetic field. Thus. the total magnetic field in the y-direction at a point (x. y) is given by: B,(x.y) = B1ylx,y) + Baylxy) where B,y(x,y) and B,y(x,y) are the y-components of the magnetic fields produced by each coil at the point (x. V). The y-component of the magnetic field produced by a single coil at point (x, y) is given by: B.y(X.y) = (no * N *I * Fl2 ' y) / (2 * ((x - d/i2)2 + yzl'3/2'D - lug * N ' | * Fl2 * y) / (2 * ((x + d/2)2 + WW2\") The y-component of the magnetic field produced by the second coil at point (x. y) is given by: Bzy(x.yl = (P0 * N ' l * R2 ' y) / (2 * (ix - d/2)2 + Win/2'\" - (uu " N * I * R2 ' y) / l2 ' (ix + d/2l2 + yzl'mlll The total magnetic field B_total(x.y) can be visualized using Desmos by inputting the following expression: B_total(x.y) = (2 * pa ' N ' | " R2 * y) / (sqrt((x - d/2)2 + y2)3 + sqrt((x + d/2)2 + yzF) Here's what the resulting magnetic field looks like between the coils (in the region x=-1 to 1 and y=-1 to 1): We can see that the magnetic field between the coils is strongest near the center, where the distance between the coils is smallest, and decreases rapidly as we move away from the center. Outside the coils, the magnetic field is approximately zero, since there are no currents flowing in that region. If we change the value of the parameter d (the separation between the coils). we can see how the magnetic field changes