Van der Waals forces and zero-point energy for dielectric and permeable materials

Abstract

It is pointed out that symmetries of Maxwell's equations under interchange of electric and magnetic fields can be exploited to convert calculations of van der Waals forces between electrically polarizable particles and dielectric materials into results for magnetically polarizable particles and permeable materials. In particular, the forces between perfectly conducting materials calculated from ideas of zero-point radiation are the same as the forces between infinitely permeable materials. Combinations of dielectric materials and permeable materials can lead to repulsive van der Waals forces. For example, two infinitely permeable parallel plates are attracted together with exactly the same force as obtained by Casimir for the van der Waals attraction between two perfectly conducting plates. On the other hand, two parallel plates of area $A$ and separation $d$, one of which is a perfect conductor and one of which is infinitely permeable, are repelled by a force $F=\frac{7}{8}\frac{{\ensuremath{\pi}}^{2}\ensuremath{\hbar}cA}{240{d}^{4}}$, differing in magnitude by a factor of $\frac{7}{8}$ from Casimir's attractive force. A calculation of the repulsive force is given based on ideas of classical electromagnetic zero-point radiation.