The board can be considered to be suffused with an electric field whose strength at position .
Each pebble carries a unit charge: white = +1, black = -1.
The net charge at square (positive, negative, or zero).
The electric force at each square equals charge × field strength = .
Across the entire board, the net force is always zero:
All operations preserve this force conservation — they rearrange charges without changing the net force.