Casimir force in non-planar geometric configurations by Cho S.N.

By Cho S.N.

The Casimir strength for charge-neutral, excellent conductors of non-planar geometric configurations were investigated. The configurations have been: (1) the plate-hemisphere, (2) the hemisphere-hemisphere and (3) the round shell. The ensuing Casimir forces for those actual preparations were discovered to be appealing. The repulsive Casimir strength discovered through Boyer for a round shell is a different case requiring stringent fabric estate of the field, in addition to the categorical boundary stipulations for the wave modes in and out of the field. the required standards indetecting Boyer's repulsive Casimir strength for a sphere are mentioned on the finish of this thesis.

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As a result, we have i=1 [νi − νT,i − νi ] eˆi = 0. In terms of the spherical coordinate representation for (ν1 , ν2 , ν3 ) and (ν1 , ν2 , ν3 ) , we can solve for θ and φ. 14) i where the notation φ` and θ` indicates that φ and θ are explicitly expressed in terms of the primed variables, respectively. 3, the hemisphere center is only shifted along yˆ by an amount of νT,2 = a, which leads to νT,i=2 = 0. Nevertheless, the derivation have been done for the case where νT,i = 0, i = 1, 2, 3 for the generalization purpose.

The notation ; R s,1 , R s,0 of k inner denotes that it is defined in terms of the initial reflection point R s,1 on the surface and the initial crossing point R s,0 of the hemisphere opening (or the sphere cross-section). The notation ; R s,1 + aRˆ s,1 of k outer implies the outer surface reflection point. The total resultant imparted momentum on the hemisphere or sphere is found by summing over all modes of wave, over all directions. 23 3. : Inside the cavity, an incident wave k i on first impact point R i induces a series of reflections that propagate throughout the entire inner cavity.

The wall has to have moved by the amount Rwall = R˙ wall t, where t is the total duration of impact, and R˙ wall is calculated from the momentum conservation and it is non-zero. 10. For that system   R˙ rp,cm,α (t0 ) = R˙ lp,3 (t0 ) + R˙ rp,2 (t0 ) , 1 pvirtual−photon = Hns , (t0 ) ,  R˙ lp,cm,α (t0 ) = R˙ rp,1 (t0 ) + R˙ lp,2 (t0 ) . c For simplicity, assuming that the impact is always only in the normal direction, R˙ rp,cm,α (t0 ) = 2 Hns ,3 (t0 ) − Hns ,2 (t0 ) , mrp c R˙ lp,cm,α (t0 ) = 2 Hns ,1 (t0 ) − Hns ,2 (t0 ) , mlp c where the differences under the magnitude symbol imply field energies from different regions counteract the other.

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