Worksheet: Charge Enclosed in a Spherically Symmetric Region

In this worksheet, we will practice using Gauss' law to relate the electric flux through a closed surface to the amount of charge enclosed by that surface.

Q1:

The electric flux through a spherical surface is 4.0×10 N⋅m2/C. What is the net charge enclosed by the surface?

  • A 5 . 0 × 1 0 C
  • B 2 . 8 × 1 0 C
  • C 2 . 1 × 1 0 C
  • D 4 . 1 × 1 0 C
  • E 3 . 5 × 1 0 C

Q2:

A charge of +3.0 µC is put on the surface of a hollow aluminum spherical ball which has a radius of 5.0 cm. The charge is in equilibrium at the outer surface of the ball.

Determine the magnitude of the electric field produced by this charge at a point 1.0 cm from the center of the aluminum ball.

  • A 1 . 8 × 1 0 N/C
  • B0 N/C
  • C 2 . 5 × 1 0 N/C
  • D 4 . 0 × 1 0 N/C
  • E 0 . 7 2 × 1 0 N/C

Determine the magnitude of the electric field produced by this charge at a point 10 cm from the center of the aluminum ball.

  • A0 N/C
  • B 1 . 3 × 1 0 N/C
  • C 2 . 3 × 1 0 N/C
  • D 1 . 6 × 1 0 N/C
  • E 2 . 7 × 1 0 N/C

Q3:

A charge of 30 µC is distributed uniformly over the surface of a spherical volume of radius 10.0 cm.

Determine the electric field due to this charge at a distance of 2.0 cm from the center of the sphere.

  • A 2 . 3 × 1 0 r N/C
  • B 1 . 5 × 1 0 r N/C
  • C0 N/C
  • D 7 . 6 × 1 0 r N/C
  • E 3 . 0 × 1 0 r N/C

Determine the electric field due to this charge at a distance of 5.0 cm from the center of the sphere.

  • A 3 . 0 × 1 0 r N/C
  • B 4 . 1 × 1 0 r N/C
  • C0 N/C
  • D 2 . 3 × 1 0 r N/C
  • E 1 . 1 × 1 0 r N/C

Determine the electric field due to this charge at a distance of 20.0 cm from the center of the sphere.

  • A 6 . 7 × 1 0 r N/C
  • B 3 . 2 × 1 0 r N/C
  • C0 N/C
  • D 1 . 5 × 1 0 r N/C
  • E 9 . 0 × 1 0 r N/C

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