Unformatted text preview: ~ r ) = X ~ G V ~ G exp( i ~ G · ~ r ) (4) which can be written in terms of the ρ ~ G as, V ( ~ r ) = X ~ G ρ ~ G G 2 exp( i ~ G · ~ r ) (5) with G 2 = ~ G · ~ G . Hint: Consider the Poisson equation. c) Show that for a point charge at ~ r and its periodic images, that ρ ~ G = 1 Ω exp(i ~ G~ r ) with Ω = L 3 . d) Determine an expression for the total electrostatic energy density. Explain why ρ ~ G =0 must be zero in order for the answer to be sensible. What does this imply for ρ ( ~ r )? 1...
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 Fall '08
 Johnson,M
 Electrostatics, Electric charge, Fundamental physics concepts, Energy density, Reciprocal lattice, periodic charge density

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