Energy and force between two magnetic nanotubes

The interaction energy and force between two parallel thin magnetic nanotubes is calculated using four different approaches. Although they agree for separation distances over 10 times the radius of any tube, some differences appear for shorter distances. Two exact methods giving identical results face handling difficulties in comparison with an approximate method based on a truncated expansion which produces fair enough results for distances to be found in the range of interest. Numerical calculations are done for cobalt particles of dimensions corresponding to nanotubes already manufactured and with properties reported in the literature. The force between two identical and parallel Co nanotubes (L = 60 μ m, D = 180 nm), separated by a distance of 300 nm is of the order of few microdynes.