Worksheet: Calculating the Net Electric Field of Multiple Point Charges

In this worksheet, we will practice calculating the resultant electric fields produced by multiple charges and their vectors.

Q1:

Two equal sized charged spheres, Sphere A and Sphere B have charges of +π‘žοŠ§ and βˆ’π‘žοŠ¨ respectively. The spheres are separated by a straight-line distance 𝑑. The net electric field produced by spheres has a null point along 𝑑 at a distance of 𝑑4 m from Sphere A. What is the ratio of the magnitude of the charge of Sphere B to that of Sphere A?

  • A π‘ž  = 3π‘žοŠ§
  • B π‘ž  = 9π‘žοŠ§
  • C π‘ž  = 4π‘žοŠ§
  • D π‘ž  = 2π‘žοŠ§
  • E π‘ž  = 8π‘žοŠ§

Q2:

Point charges π‘ž=+50¡C and π‘ž=βˆ’25¡C are placed 1.0 m apart. The point 𝑃 is at the midpoint of the two charges’ positions.

What is the magnitude of the electric field produced by the charges at 𝑃?

  • A 2 . 1 Γ— 1 0  N/C
  • B 2 . 7 Γ— 1 0  N/C
  • C 2 . 9 Γ— 1 0  N/C
  • D 2 . 3 Γ— 1 0  N/C
  • E 2 . 5 Γ— 1 0  N/C

What magnitude force would act on a charge π‘ž=20¡C if it was located at 𝑃?

Q3:

Two fixed point charges each have magnitudes of 4.0Γ—10 C. The charges are located on the π‘₯-axis at the positions π‘₯=3.0m and π‘₯=βˆ’3.0m. A charge 𝑄 is placed at the origin and the resultant electric field of the three charges is zero at a point on the 𝑦-axis where 𝑦=3.0m. Find the magnitude of 𝑄.

  • A 2 . 8 Γ— 1 0   C
  • B 2 . 1 Γ— 1 0   C
  • C 3 . 5 Γ— 1 0   C
  • D 4 . 3 Γ— 1 0   C
  • E 5 . 0 Γ— 1 0   C

Q4:

Point charges are placed at the four corners of a rectangle as shown. The charges’ magnitudes are: π‘ž=+2.0Γ—10,π‘ž=βˆ’2.0Γ—10,π‘ž=+4.0Γ—10,π‘ž=+1.0Γ—10.οŠͺCCCC What is the electric field in the plane of the rectangle at the point 𝑃?

  • A ο€Ή 4 . 9 Γ— 1 0 + 1 . 2 Γ— 1 0    i j N/C
  • B ο€Ή 9 . 4 Γ— 1 0 + 1 . 5 Γ— 1 0    i j N/C
  • C ο€Ή 6 . 9 Γ— 1 0 + 2 . 1 Γ— 1 0    i j N/C
  • D ο€Ή 4 . 6 Γ— 1 0 + 1 . 1 Γ— 1 0    i j N/C
  • E ο€Ή 6 . 4 Γ— 1 0 + 1 . 5 Γ— 1 0    i j N/C

Q5:

Point charges 𝑄=33.2¡C and 𝑄=56.0¡C are placed 0.85 m apart along a line 𝐿.

How far from π‘„οŠ§ along 𝐿 does the net electric field, due to the charges, equal zero?

What is the magnitude of the electric field due to the charges at the midpoint of 𝐿?

  • A 0 . 2 3 Γ— 1 0  N/C
  • B 1 . 8 Γ— 1 0  N/C
  • C 0 . 7 1 Γ— 1 0  N/C
  • D 1 . 1 Γ— 1 0  N/C
  • E 0 . 8 7 Γ— 1 0  N/C

Q6:

Two fixed charges of +30 mC and βˆ’15 mC, respectively, are separated horizontally by a distance of 12.0 cm. Four points of interest, π‘ƒοŠ§, π‘ƒοŠ¨, π‘ƒοŠ©, and 𝑃οŠͺ, have positions relative to the fixed charges, as shown in the diagram.

Find the net potential due to the charges at π‘ƒοŠ§.

Find the net potential due to the charges at π‘ƒοŠ¨.

Find the net potential due to the charges at π‘ƒοŠ©.

Find the net potential due to the charges at 𝑃οŠͺ.

Q7:

Two charged particles π‘„οŠ§ and π‘„οŠ¨ each has a charge of 2.50 Β΅C. The particles are placed symmetrically along the π‘₯-axis, each at a distance of 3.84 cm from the origin. Another charged particle π‘„οŠ© with a charge of 4.47 Β΅C and a mass of 13.0 mg is initially held at rest 2.76 cm vertically above the origin and then released. What is the speed of π‘„οŠ© when it is at a point 4.36 cm vertically above the origin?

Q8:

What is the electric field vector at the midpoint 𝑀 given that π‘ž=6.0Β΅C and π‘Ž=20.0cm as shown?