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.

Q1:

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.

  • A 5 . 0 × 1 0 N⋅m2/C
  • B 2 . 1 × 1 0 N⋅m2/C
  • C 1 . 1 × 1 0 N⋅m2/C
  • D 2 . 5 × 1 0 N⋅m2/C
  • E 1 . 5 × 1 0 N⋅m2/C

Q2:

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?

  • A 8 . 0 × 1 0 C
  • B 6 . 6 × 1 0 C
  • C 9 . 6 × 1 0 C
  • D 6 . 0 × 1 0 C
  • E 8 . 9 × 1 0 C

Q3:

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).

  • A 3 . 6 × 1 0 N⋅m2/C
  • B 3 . 4 × 1 0 N⋅m2/C
  • C 2 . 6 × 1 0 N⋅m2/C
  • D 3 . 0 × 1 0 N⋅m2/C
  • E 4 . 0 × 1 0 N⋅m2/C

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

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

  • A 3 . 6 × 1 0 N⋅m2/C
  • B 2 . 3 × 1 0 N⋅m2/C
  • C 3 . 3 × 1 0 N⋅m2/C
  • D 3 . 0 × 1 0 N⋅m2/C
  • E0 N⋅m2/C

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

Q4:

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.

  • A 6 . 3 3 × 1 0 N⋅m2/C
  • B 4 7 . 1 × 1 0 N⋅m2/C
  • C 2 8 . 3 × 1 0 N⋅m2/C
  • D 4 5 . 2 × 1 0 N⋅m2/C
  • E 6 . 5 5 × 1 0 N⋅m2/C

Q5:

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?

  • A 6 3 × 1 0 N⋅m2/C
  • B 2 . 3 × 1 0 N⋅m2/C
  • C 1 2 × 1 0 N⋅m2/C
  • D 6 . 0 × 1 0 N⋅m2/C
  • E 4 . 2 × 1 0 N⋅m2/C

Q6:

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?

  • A 4 . 7 × 1 0 C
  • B 4 . 2 × 1 0 C
  • C 6 . 4 × 1 0 C
  • D 1 . 6 × 1 0 C
  • E 6 . 2 × 1 0 C

Q7:

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?

  • A 1 . 5 × 1 0 C
  • B 2 . 5 × 1 0 C
  • C 1 . 2 × 1 0 C
  • D 1 5 × 1 0 C
  • E 1 4 × 1 0 C

Q8:

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?

  • A 4 . 3 × 1 0 m/s2
  • B 9 . 5 × 1 0 m/s2
  • C 7 . 1 × 1 0 m/s2
  • D 7 . 6 × 1 0 m/s2
  • E 4 . 6 × 1 0 m/s2

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