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.

  • A1.8×10 N/C
  • B3.9×10 N/C
  • C2.6×10 N/C
  • D3.6×10 N/C
  • E3.1×10 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?

  • A4.1×10 V/m
  • B3.0×10 V/m
  • C4.5×10 V/m
  • D3.7×10 V/m
  • E3.3×10 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?

  • A4.4×10 N/m
  • B1.8×10 N/m
  • C2.1×10 N/m
  • D3.5×10 N/m
  • E1.3×10 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?

  • A96×10 N/C
  • B1.7×10 N/C
  • C13×10 N/C
  • D1.1×10 N/C
  • E69×10 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?

  • A0.97×10 N
  • B40×10 N
  • C95×10 N
  • D12×10 N
  • E3.2×10 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?

  • A7.9×10 N
  • B9.6×10 N
  • C8.2×10 N
  • D14×10 N
  • E1.4×10 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.

  • A9.4×10/NC
  • B0.0/NC
  • C5.0×10/NC
  • D6.3×10/NC
  • E0.15×10/NC

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?

  • A3.25×10 N/C
  • B2.43×10 N/C
  • C123×10 N/C
  • D36.2×10 N/C
  • E2.33×10 N/C

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

  • A7.01×10 N/C
  • B35.1×10 N/C
  • C632×10 N/C
  • D68.2×10 N/C
  • E98.4×10 N/C

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