Find the vector potential inside and outside of a spherical coil (solenoid) with an equidistant right-handed winding with respect to the z-axis through which a current / flows, as a function of the coil radius r and the winding density n = dN/dz. Calculate the magnetic field as the curl of the vector potential and show that it fulfills the boundary condition at the radius of the coil. N Hint: Straightforward integration is not the best solution, look for equivalent problems, symmetries etc.