A rigid rectangular coil of mass m, width w, and N turns is suspended vertically from an ideal spring of force constant k. The bottom horizontal segment of the coil hangs in a uniform horizontal magnetic field B directed perpendicular to the plane of the coil, while the top segment remains outside the field. When a current I is established in the coil, the resulting downward magnetic force causes an additional vertical equilibrium displacement \(\Delta y\) from the coil's initial unpowered position. If a linear graph of \(\Delta y\) on the vertical axis versus I on the horizontal axis yields a line of best fit with slope S, which of the following correctly identifies what S represents and the resulting expression for B?