Worksheet: Charge Contained on a Plane Surface

In this worksheet, we will practice applying Gauss's law to planar regions of space, showing how the electric field varies around such regions.

Q1:

The electric flux through a square-shaped area of side 5.0 cm near a large charged sheet is found to be 3 . 0 0 × 1 0 5 N⋅m2/C when the area is parallel to the plate.

Find the charge density on the sheet.

  • A 3 . 1 × 1 0 1 3 C/m2
  • B 2 . 5 × 1 0 1 3 C/m2
  • C 3 . 5 × 1 0 1 3 C/m2
  • D 2 . 1 × 1 0 1 3 C/m2
  • E 3 . 9 × 1 0 1 3 C/m2

Q2:

A infinite sheet of charge has a uniform charge density of 18.0 µC/m2. What is the magnitude of the electric field due to this charge at a point just above the surface of the sheet?

  • A 4 . 6 0 × 1 0 6 N/C
  • B 0 . 3 2 2 × 1 0 6 N/C
  • C 6 . 5 5 × 1 0 6 N/C
  • D 1 . 0 2 × 1 0 6 N/C
  • E 7 . 4 0 × 1 0 6 N/C

Q3:

An aluminum foil cube of thickness 0.25 mm and cross-sectional side lengths of 13 cm has a charge of 27 µC that spreads on both of its 13 cm by 13 cm faces evenly. The charge on the other faces is negligible.

Find the charge density on the cube’s charged faces.

  • A 3 . 3 × 1 0 C/m2
  • B 1 4 × 1 0 C/m2
  • C 6 0 × 1 0 C/m2
  • D 8 . 0 × 1 0 C/m2
  • E 0 . 5 5 × 1 0 C/m2

Find the magnitude of the electric field 0.50 cm from the center of a cube’s charged face, assuming approximate planar symmetry.

  • A 9 . 0 × 1 0 N/C
  • B 4 . 3 × 1 0 N/C
  • C 1 2 × 1 0 N/C
  • D 9 . 2 × 1 0 N/C
  • E 7 . 1 × 1 0 N/C

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