HW-14 - Theory of Solids HW-14 Solution By Qifeng Shan...

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1 Theory of Solids HW-14 Solution By Qifeng Shan Ashcroft and Mermin’s book 18-1 Some Problems in Electrostatics Bearing on Potentials and the Double Layer (a) Consider a plane surface of a metal perpendicular to the x-axis. Perhaps the simplest model of the distortion in the charge densities of the cells near the surface is one that ignores any variation in the plane of the surface, describing the deviation in the charge density from its form in the bulk by a function of the single variable x , δρ ( x ). The condition that there is no net macroscopic charge density on the surface is   . 0 r  dx (18.31) The charge density δρ ( x ) will give rise to an electric field E(x) also normal to the surface. Deduce directly from Gauss’s law  4 E that if the field vanishes on one side of the double layer (as it does inside the metal) then it must also vanish on the other side. Deduce also that the work that must be done to move an electron through the double layer is just
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HW-14 - Theory of Solids HW-14 Solution By Qifeng Shan...

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