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Worksheet: Calculating the Net Electric Field of Multiple Point Charges

Q1:

Two equal sized charged spheres, Sphere A and Sphere B have charges of + π‘ž 1 and βˆ’ π‘ž 2 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 𝑑 4 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 2 = 3 π‘ž 1
  • B π‘ž 2 = 2 π‘ž 1
  • C π‘ž 2 = 4 π‘ž 1
  • D π‘ž 2 = 9 π‘ž 1
  • E π‘ž 2 = 8 π‘ž 1

Q2:

Point charges π‘ž = + 5 0 1 Β΅ C and π‘ž = βˆ’ 2 5 2 Β΅ 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 . 3 Γ— 1 0 βˆ’ 6 N/C
  • B 2 . 1 Γ— 1 0 βˆ’ 6 N/C
  • C 2 . 5 Γ— 1 0 βˆ’ 6 N/C
  • D 2 . 7 Γ— 1 0 βˆ’ 6 N/C
  • E 2 . 9 Γ— 1 0 βˆ’ 6 N/C

What magnitude force would act on a charge π‘ž = + 3 0 3 Β΅ C if it was located at 𝑃 ?

Q3:

Two fixed point charges each have magnitudes of 4 . 0 Γ— 1 0 βˆ’ 6 C. The charges are located on the π‘₯ -axis at the positions π‘₯ = 3 . 0 m and π‘₯ = βˆ’ 3 . 0 m . 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 . 0 m . Find the magnitude of 𝑄 .

  • A 3 . 5 Γ— 1 0 βˆ’ 6 C
  • B 2 . 1 Γ— 1 0 βˆ’ 6 C
  • C 4 . 3 Γ— 1 0 βˆ’ 6 C
  • D 2 . 8 Γ— 1 0 βˆ’ 6 C
  • E 5 . 0 Γ— 1 0 βˆ’ 6 C

Q4:

Point charges are placed at the four corners of a rectangle as shown. The charges’ magnitudes are: What is the electric field in the plane of the rectangle at the point 𝑃 ?