The external magnetic field created by the superposition of identical parallel finite solenoids

We use superposition and numerical methods to show that the external magnetic field generated by parallel identical solenoids can be nearly uniform and substantial, even when the solenoids have lengths that are large compared to their radii. We examine both a ring of solenoids and a large hexagonal array of solenoids. In both cases, we discuss how the magnitude and uniformity of the external field depend on the length of and the spacing between the solenoids. We also discuss some novel properties of a single solenoid, e.g., that even for short solenoids the energy stored in the internal magnetic field exceeds the energy stored in the spatially infinite external magnetic field. These results should be broadly interesting to undergraduates learning about electricity and magnetism.