THE FIELDS OF MOVING CHARGES — Edward Purcell & David Morin
Physics — E&M · infinite-square-lattice
Problem
Infinite square lattice **
Consider a two-dimensional infinite square lattice of 1 Ω resistors. That is, every lattice point in the plane has four 1 Ω resistors connected to it. What is the equivalent resistance between two adjacent nodes? This problem is a startling example of the power of symmetry and superposition. Hint: If you can determine the voltage drop between two adjacent nodes when a current of, say, 1 A goes in one node and comes out the other, then you are done. Consider this setup as the superposition of two other setups.