a Show that the Casimir force from the vacuum energy of Fermions has the

A show that the casimir force from the vacuum energy

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which are sometimes known as Lifshitz forces.a) Show that the Casimir force from the vacuum energy of Fermions has the oppositesign than from bosons.b) The vacuum energy of massive particles also contributes to the Casimir force.Before doing the calculation, how do you expect the Casimir force to depend onmass? Now do the calculation and see if you are correct (use any approximationsyou want).c) Some people have proposed that geckos use the Casimir force to climb walls. It isknown that gekkos do not use suction (like salamanders) or capillary adhesion (likesome frogs). A gecko’s foot is made of a million tiny hairs called setae which ter-minate in spatula shaped structures around 0.5μmwide. Use dimensional analysisand the form of the Casimir force to decide whether you think this could be pos-sible. Treat this as a Fermi problem – estimate everything you don’t know. Forexample, you might assume that the hairs can get within molecular spacings of thewall the gekko is climbing. Page 2/2
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