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The Casimir Effect

The Casimir Effect. What is the Casimir Effect?. Attractive force between two uncharged parallel plates F=( π hcA)/(480d 4 ) Discovered by H.B.G. Casimir in 1948 Caused by the restriction of electromagnetic modes E=0 at surface of each conductor (think waves on a string)

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The Casimir Effect

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  1. The Casimir Effect

  2. What is the Casimir Effect? • Attractive force between two uncharged parallel plates • F=(πhcA)/(480d4) • Discovered by H.B.G. Casimir in 1948 • Caused by the restriction of electromagnetic modes • E=0 at surface of each conductor (think waves on a string) • As the plates are moved together, fewer modes are viable • With fewer modes available, the energy density of the space between the plates becomes less than the surrounding vacuum • Lower energy density means there must be a force pulling the plates together.

  3. Comparison of Forces • Consider a parallel plate capacitor with area A=0.01m2 and the distance between them, d, to be 0.01m. The voltage, V, between them is 30V

  4. Comparison of Forces • Consider a parallel plate capacitor with area A=0.01m2 and the distance between them, d, to be 0.01m. The voltage, V, between them is 30V • Electric Force: • Q=CV • C=ε0A/d, • V=Ed • F=EQ=V2C/d=(V2 ε0A)/d2 • F=7.97*10-7 N

  5. Comparison of Forces • Consider a parallel plate capacitor with area A=0.01m2 and the distance between them, d, to be 0.01m. The voltage, V, between them is 30V. • Now, Consider the same plates, but with no potential difference between them. • Casimir Force • F=(πhcA)/(480d4) • F=1.30*10-21 N

  6. Comparison of Forces • Consider a parallel plate capacitor with area A=0.01m2 and the distance between them, d, to be 0.01m. The voltage, V, between them is 30V. • Now, Consider the same plates, but with no potential difference between them. Lets make a rough comparison of the gravitational force by approximating them as point masses and saying that each plate has a mass of 0.1kg. • Gravitational Force • F=Gm2/d2 • F=6.67*10-9 N • But, because of the 1/r4 dependence, if d is very very small then the Casimir force will start to dominate.

  7. Forces Why is the Casimir force is attractive? E field - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - +

  8. Why is the Casimir force is attractive? - + - + -- ++ -- ++ - + - + - + - + - + -- ++ -- ++ - + + - + Forces e- e+ e- e+ Image Particles Image Particles

  9. Measurement of the Casimir Force • Problems • Casimir force is very weak • Has a very short range (1/r4 dependence) • Plates must be parallel • First tentative experiments done by in 1958 (Spaarnay) • In 1997, the technique of using a spherical “plate” with large radius overcame the problem of keeping the plates parallel. (Lamoreaux)

  10. Real World Applications • Microelectromechanical systems (MEMS) • Used in the manufacture of car airbag systems • Casimir Force can make parts of MEMS stick together • Casimir Force can also be used to control the movement of MEMS devices

  11. References • “The Casimir effect: a force from nothing” from the September 2002 issue of Physics World • “Resource Letter CF-1: Casimir Force” by S.K. Lamorceaux from the American Journal of Physics 67 (10) (October 1999) • “Essentials of the Casimir effect and its computation” by E. Elizalde and A. Romeo from the American Journal of Physics 59 (8) (August 1991)

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