# Infinite Resistive lattice problem

While there have been many discussions regarding the solution(say using the Fourier transform or the lattice Green's function approach) to the two-point resistance of an infinite-square resistive lattice my doubt is actually related to one thing common to almost all the approaches to the problem i.e how does having applied a unit current and removed the same current between the points on which one wants to determine the effective resistance between, imply that the currents at the other nodes are zero.Moreover in order to obtain the difference equation (discretized Laplacian) one makes use of the Kirchoff's current law(which talks about the current in the branches connecting neighboring nodes).

So say i applied a unit current, $I_{m,n}=\delta_{m,mo}\delta_{n,no}- \delta_{m,0}\delta_{n,0}$ at the $(m,n)$th point on the lattice. In order to use my KCL i would need talk about the current in the branches which are incident at the point/node (m,n).So this means that the current emanates from point $A$ and reaches $B$, $C$, $D$ and $E$. But then as soon as it reaches those points does it become zero??

But this doesn't make sense right since we are removing the same unit current from another point(different from the m,nth point on the lattice) in this case from node $O$.

Could someone resolve the same for me.

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Related: physics.stackexchange.com/q/2072/2451 , physics.stackexchange.com/q/10308/2451 and links therein. – Qmechanic Apr 23 '14 at 21:44

Current flowing point $A$ will reach point $B$ from four different directions, not just the direct route. And because charge can't build up anywhere, the sum of all the currents reaching $B$ has to be zero. – lionelbrits Dec 21 '14 at 23:10