Worksheet: Charge Enclosed in a Cylindrically Symmetric Region

In this worksheet, we will practice using Gauss's law to find the electric field around a cylindrically symmetric distribution of charge.

Q1:

The electric field at 2.0 cm from the center of long copper rod of radius 1.0 cm has a magnitude 3.0 N/C and is directed outward from the axis of the rod.

What is the charge per unit length of the copper rod?

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

What would be the electric flux through a cube of side 5.0 cm situated such that the rod passes through opposite sides of the cube perpendicularly?

  • A0.012 N⋅m2/C
  • B0.027 N⋅m2/C
  • C0.0090 N⋅m2/C
  • D0.022 N⋅m2/C
  • E0.019 N⋅m2/C

Q2:

An infinitely long copper cylindrical shell of inner radius 4.0 cm and outer radius 7.0 cm concentrically surrounds an infinitely long charged aluminum rod of radius 2.0 cm with a charge density of 5.0 pC/m. All charges on the aluminum rod reside at its surface. The inner surface of the cylindrical shell has an exactly opposite charge to that of the aluminum rod, while the outer surface of the cylindrical shell has the same charge as the aluminum rod.

Find the magnitude of the electric field 1.0 cm from the center of the aluminum rod.

Find the magnitude of the electric field 3.0 cm from the center of the aluminum rod.

Find the magnitude of the electric field 5.0 cm from the center of the aluminum rod.

Find the magnitude of the electric field 8.0 cm from the center of the aluminum rod.

  • A 9 . 2 × 1 0 N/C
  • B 5 . 3 × 1 0 N/C
  • C 1 . 1 × 1 0 N/C
  • D 6 . 2 × 1 0 N/C
  • E0.0 N/C

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