Charge Density

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 sA. Piece B is the other 1/4 of the sheet, with charge density sB.

Rank these three charge densities from largest to smallest.

  1. σ = σA = σB
  2. σ > σA > σB
  3. σB > σA > σ
  4. σ > σA = σB
  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.