1. The problem statement, all variables and given/known data A rectangular coil is composed of 150 turns of a filamentary conductor. Find the mutual inductance in free space between this coil and an infinite straight filament on the z axis if the four corners of the coil are located at 2. Relevant equations B = (phi-hat) μoI/2πr dS = (n-hat) dydz Φ = ∫B⋅dS 3. The attempt at a solution I can easily solve this problem if the coil is parallel to the y-z plane and x = 1 since the r in the formula varies only on y thus, becomes sqrt(y2 + 1) then convert phi-hat to cartesian unit vectors and the area unit vector is just -(x-hat). Now, in this problem, I have converted the area unit vector to its cartesian unit vector. I am confused on how I will write the expression for r since it now varies on x, y, and z?