Current-sheet solenoid solved in closed form, B(z) = (mu0*n*I/2)*[(L/2-z)/sqrt(R^2+(L/2-z)^2) + (L/2+z)/sqrt(R^2+(L/2+z)^2)], which at the centre reduces to mu0*N*I/sqrt(L^2+D^2). Air core (mu_r = 1), single layer, on-axis only. The turn-count floor below which the closed form is more than 1% from a real discrete winding is measured against an independent Biot-Savart sum over the individual turns, not against a rearrangement of the same formula. Pure mathematics - nothing is fetched and nothing is recalled.
Open this on MakerPortal · Free to reuse with attribution