For a perfectly conducting cylinder, the M and E polarizations correspond to Dirichlet and Neumann scalar fields:

  Can be used to compute the interaction between a cylinder and a plate:

  "Casimir Interaction between a Plate and a Cylinder,"

T. Emig, R.L. Jaffe, M. Kardar & Scardicchio, Phys. Rev. Lett. 96, 080403 (2006)

  Limiting force for a thin wire (R >> H ):

due to long wave-length charge fluctuations along the length of the cylinder.

Unexpected non-monotonicity due to three-body effects:

"Nonmonotonic effects of parallel sidewalls on Casimir forces between cylinders,"

Rahi, Rodriguez, Emig, Jaffe, Johnson,  & Kardar, Phys. Rev. A 77, 030101(R) (2008)