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.


Two equally 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?

  • Aπ‘ž=3π‘žοŠ¨οŠ§
  • Bπ‘ž=9π‘žοŠ¨οŠ§
  • Cπ‘ž=4π‘žοŠ¨οŠ§
  • Dπ‘ž=2π‘žοŠ¨οŠ§
  • Eπ‘ž=8π‘žοŠ¨οŠ§


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?

  • A2.1Γ—10 N/C
  • B2.7Γ—10 N/C
  • C2.9Γ—10 N/C
  • D2.3Γ—10 N/C
  • E2.5Γ—10 N/C

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


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.

  • A2.8Γ—10 C
  • B2.1Γ—10 C
  • C3.5Γ—10 C
  • D4.3Γ—10 C
  • E5.0Γ—10 C


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?

  • Aο€Ή4.9Γ—10+1.2Γ—10ο…οŠ¬οŠ­ij N/C
  • Bο€Ή9.4Γ—10+1.5Γ—10ο…οŠ¬οŠ­ij N/C
  • Cο€Ή6.9Γ—10+2.1Γ—10ο…οŠ¬οŠ­ij N/C
  • Dο€Ή4.6Γ—10+1.1Γ—10ο…οŠ¬οŠ­ij N/C
  • Eο€Ή6.4Γ—10+1.5Γ—10ο…οŠ¬οŠ­ij N/C


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?

  • A0.23Γ—10 N/C
  • B1.8Γ—10 N/C
  • C0.71Γ—10 N/C
  • D1.1Γ—10 N/C
  • E0.87Γ—10 N/C


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.


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?


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

  • A(3.2+3.7)Γ—10ij N/C
  • B(3.8βˆ’3.8)Γ—10ij N/C
  • C(4.2βˆ’3.8)Γ—10ij N/C
  • D(3.8+3.8)Γ—10ij N/C
  • E(96+21)Γ—10ij N/C

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