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.

1. σ = σ_A = σ_B
2. σ > σ_A > σ_B
3. σ_B > σ_A > σ
4. σ > σ_A = σ_B
5. 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.