Worksheet: The Electric Field of a Line of Charge

In this worksheet, we will practice calculating the electric field around a uniform linear charge distribution that is modeled as a set of line segments.

Q1:

A long, straight wire has a uniform linear charge density of 4.0×10 C/m. Calculate the magnitude of the electric field strength at a perpendicular distance of 2.0 m from the axis of the wire.

  • A 1 . 8 × 1 0 N/C
  • B 3 . 9 × 1 0 N/C
  • C 2 . 6 × 1 0 N/C
  • D 3 . 6 × 1 0 N/C
  • E 3 . 1 × 1 0 N/C

Q2:

A very long, thin wire has a uniform linear charge density of 50 µC/m. What is the magnitude of the electric field 2.0 cm from the axis of the wire?

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

Q3:

A long cylinder of aluminum of radius 0.25 meters is charged so that it has a uniform charge per unit length on its surface of 𝜆=2.5×10 C/m. A point 𝑃 is located along a line normal to the cylinder’s axis, 0.15 m from the axis.

What is the magnitude of the electric field at point 𝑃?

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

What is the electric potential at point 𝑃?

  • A640 kV
  • B760 kV
  • C830 kV
  • D550 kV
  • E710 kV

Q4:

The linear charge density of the thin semicircular wire shown is 0.030 C/m. The wire forms an arc with radius 𝑟=0.500m. What is the magnitude of the electric field at the point P?

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

Q5:

The semicircle of thin wire shown in the diagram has a radius 𝑅=55.0cm and the charge per unit length of the wire is 0.0063 C/m. What magnitude of electric force is exerted by the wire on a point particle with charge 𝑞=3.0µC that is located at the center of the semicircle?

  • A 0 . 9 7 × 1 0 N
  • B 4 0 × 1 0 N
  • C 9 5 × 1 0 N
  • D 1 2 × 1 0 N
  • E 3 . 2 × 1 0 N

Q6:

A thin rod has a linear charge density of 0.0022 C/m. What is the magnitude of the electric force on the point charge 𝑞=9.0µC, knowing that 𝑎=10cm and 𝐿=40cm?

  • A 7 . 9 × 1 0 N
  • B 9 . 6 × 1 0 N
  • C 8 . 2 × 1 0 N
  • D 1 4 × 1 0 N
  • E 1 . 4 × 1 0 N

Q7:

A infinite silver rod of radius 5.0 cm has a charge of 8.0/µCcm on its surface.

Find the magnitude of the electric field at a point 9.5 cm from the center of the rod.

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

Find the magnitude of the electric field at a point 4.8 cm from the center of the rod.

Q8:

Two parallel rods of infinite length each carries a uniform charge density 𝜆=0.00130/Cm as shown in the diagram, in which the rods are seen in cross-section. The distance between the rods 𝑎=5.000cm.

What is the magnitude of the net electric field from the rods at the point 𝑃?

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

What is the magnitude of the net electric field from the rods at the point 𝑃?

  • A 7 . 0 1 × 1 0 N/C
  • B 3 5 . 1 × 1 0 N/C
  • C 6 3 2 × 1 0 N/C
  • D 6 8 . 2 × 1 0 N/C
  • E 9 8 . 4 × 1 0 N/C

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