Applying Gauss' Law correctly involves finding the charge enclosed by a surface, which often involves a charge density.

Consider, for instance, a sheet of charge with a uniform charge density σ.

The sheet is then broken into two pieces. Piece A represents 3/4 of the original sheet and has charge density s_{A}. Piece B is the other 1/4 of the sheet, with charge density s_{B}.

Rank these three charge densities from largest to smallest.

- σ = σ
_{A}= σ_{B} - σ > σ
_{A}> σ_{B} - σ
_{B}> σ_{A}> σ - σ > σ
_{A}= σ_{B} - some other order

The charge densities are all the same. Piece A has 3/4 of the original charge in 3/4 of the original area, so the charge/area is the same as that of the whole sheet. A similar argument applies to piece B.