  Using superposition and numerical approximations of a published analytical
expression for the magnetic field generated by a finite solenoid, we show that
the magnetic field external to parallel identical solenoids can be nearly
uniform and substantial, even when the solenoids have lengths that are large
compared to their radii. We study two arrangements of solenoids---a ring of
parallel solenoids whose surfaces are tangent to a common cylindrical surface
and to nearest neighbours, and a large finite hexagonal array of parallel
solenoids---and summarize how the magnitude and uniformity of the resultant
external field depend on the solenoid length and distances between solenoids.
We also report some novel results about single solenoids, e.g., that the energy
stored in the internal magnetic field exceeds the energy stored in the
spatially infinite external magnetic field for even short solenoids. These
results should be broadly interesting to undergraduates learning about
electricity and magnetism as novel examples of superposition based on a
familiar source of magnetic fields.
