Electric potential energy in an infinite 2d crystal

[Istvan]

So.. we've got a 2D crystal, corresponding an infinite square net with +-e0 charges in each one (see the atached photo). Now I'd like to calculate the constant k..when r goes to infinity... We = k (+-e0)*(+-e0)/(4 pi eps0 r)..on the positive charge in the center caused by the negative and positive charges around him in the net. It's teoretically impossible to sum infinite number of terms, but the constant k will converge to the final result. So I'd like some help how to calculate that... thanks.

 

[mda]

'madelung constant' on wikipedia is a starting point

 

[Istvan]

thanks

and what is the madelung constant for a 2d arrangement