A large coil of radius R1 and having N1 turns is coaxial with a small coil of radius R2 and having N2 turns. The centers of the coils are separated by a distance x that is much larger than R1 and R2. What is the mutual inductance of the coils? Suggestion: John von Neumann proved that the same answer must result from considering the flux through the first coil of the magnetic field produced by the second coil, or from considering the flux through the second coil of the magnetic field produced by the first coil. In this problem it is easy to calculate the flux through the small coil, but it is difficult to calculate the flux through the large coil, because to do so you would have to know the magnetic field away from the axis.