Worksheet: Gauss’s Law

In this worksheet, we will practice relating the electric flux through a closed surface to the charge contained by that surface.


A point charge of 10 µC is at an unspecified location inside a cube of side length 2.0 cm. Find the net electric flux through the surfaces of the cube.

  • A5.0×10 N⋅m2/C
  • B2.1×10 N⋅m2/C
  • C1.1×10 N⋅m2/C
  • D2.5×10 N⋅m2/C
  • E1.5×10 N⋅m2/C


The electric field in a region is given by Ei=𝑎(𝑏+𝑐𝑥), where 𝑎=200/NmC, 𝑏=2.0m, and 𝑐=2.0. What is the net charge enclosed by the shaded volume shown?

  • A8.0×10 C
  • B8.9×10 C
  • C6.0×10 C
  • D9.6×10 C
  • E6.6×10 C


The cross-sections of the closed surfaces (a), (b), (c), and (d), are shown in the accompanying diagrams.

Find the electric flux through the closed surface (a).

  • A3.6×10 N⋅m2/C
  • B3.4×10 N⋅m2/C
  • C2.6×10 N⋅m2/C
  • D3.0×10 N⋅m2/C
  • E4.0×10 N⋅m2/C

Find the electric flux through the closed surface (b).

Find the electric flux through the closed surface (c).

  • A3.6×10 N⋅m2/C
  • B2.3×10 N⋅m2/C
  • C3.3×10 N⋅m2/C
  • D3.0×10 N⋅m2/C
  • E0 N⋅m2/C

Find the electric flux through the closed surface (d).


Two large rectangular aluminum plates of area 200 cm2 face each other with a space between them. The facing areas of the plates are charged with equal amounts of opposite charges, totaling 40.0 µC. Find the flux through a circle of radius 2.00 cm between the plates when the normal to the circle makes an angle of 5.00 with a line perpendicular to the faces of the plates.

  • A6.33×10 N⋅m2/C
  • B47.1×10 N⋅m2/C
  • C28.3×10 N⋅m2/C
  • D45.2×10 N⋅m2/C
  • E6.55×10 N⋅m2/C


A point charge of 12 µC is located at the center of a cube. If there are no other charges present, what is the electric flux through one face of the cube?

  • A63×10 N⋅m2/C
  • B2.3×10 N⋅m2/C
  • C12×10 N⋅m2/C
  • D6.0×10 N⋅m2/C
  • E4.2×10 N⋅m2/C


The electric flux through a side of a cubical box is 8.8×10 N⋅m2/C. What is the total charge enclosed by the box?

  • A4.7×10 C
  • B4.2×10 C
  • C6.4×10 C
  • D1.6×10 C
  • E6.2×10 C


There is a net inward electric flux of 1.7×10 N⋅m2/C through the surface of a sphere of radius 8.5 cm. How much charge is inside the sphere?

  • A1.5×10 C
  • B2.5×10 C
  • C1.2×10 C
  • D15×10 C
  • E14×10 C


Consider a uranium nucleus to be sphere of radius 7.4×10 m with a charge of 92𝑒 distributed uniformly throughout its volume. An electron is located 4.5×10 m from the center of the nucleus.

What is the magnitude of the electric force exerted on an electron?

What is the magnitude of the acceleration of the electron?

  • A4.3×10 m/s2
  • B9.5×10 m/s2
  • C7.1×10 m/s2
  • D7.6×10 m/s2
  • E4.6×10 m/s2

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