**Cylinder-Plate geometry **

H.B.G.
Casimir and D. Polder, Phys. Rev. **73**, 360 (1948)

"The Influence of Retardation on the London-van der Waals Forces"

For asymptotically large separations

H, the attractive force between a sphere (radiusR) and a plate is

Sukenik, Boshier, Cho, Sandoghdar, and

Hinds, Phys. Rev. Lett.70, 560 (1993)"Measurement of the Casimir-Polder force"

from deflection of sodium atoms passing through a cavity.

What is the force between a metallic cylinder (wire) and a plate?

Analogy with parallel plates suggests an energy proportional to area:

Analogy with the Casimir-Polder results suggests (in the limit

R << H):

Proximity force approximation (exact in the limit

R >> H) gives:

We find the following exact results (in the limit

R >> H):

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

Emig, Jaffe, Kardar, & Scardicchio, Phys. Rev. Lett.

96, 080403 (2006).

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.

A77, 030101(R) (2008)