A capacitor is constructed from two square plates of sides and separation d, as suggested in Figure

A capacitor is constructed from two square plates of sides ℓ and separation d, as suggested in Figure P26.64. You may assume that d is much less than ℓ. The plates carry charges +Q 0 and -Q 0. A block of metal has a width ℓ, a length ℓ, and a thickness slightly less than d. It is inserted a distance x into the capacitor. The charges on the plates are not disturbed as the block slides in. In a static situation, a metal prevents an electric field from penetrating inside it. The metal can be thought of as a perfect dielectric, with 1: 0.
(a) Calculate the stored energy as a function of x.
(b) Find the direction and magnitude of the force that acts on the metallic block.
(c) The area of the advancing front face of the block is essentially equal to ℓ d. considering the force on the block as acting on this face; find the stress (force per area) on it.
(d) For comparison, express the energy density in the electric field between the capacitor plates in terms of Q0, ℓ, d, and )0.

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