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where <math>r</math> is the distance in the ''xy''-plane from the line of charge, <math>L_B</math> is the width of the material in the z direction. The superscript 2 indicates that the [[Dirac delta function]] is in two dimensions. The propagator is
<math display="block">D\left ( k \right )\mid_{k_0=0}\; = \; \frac{1}{\vec k^2 + k_{Ds}^2}</math>
where <math>k_{Ds} </math> is either the inverse [[Debye–Hückel equation|
The interaction energy is
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