Worksheet: Coulomb's Law

In this worksheet, we will practice calculating the forces that electrically charged objects exert on each other, including the net force from multiple charges.

Q1:

An object with a charge of 1.20 C is located 4.50 m away from a second object that has a charge of 0.360 C. Find the electrical force that the objects exert on each other. Use 8 . 9 8 8 × 1 0 N⋅m2/C2 for the value of Coulomb’s constant. Answer to three significant figures.

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

Q2:

Coulomb’s law defines the electrical force, 𝐹 , that two positively charged objects with the charges 𝑞 and 𝑞 exert on each other. The law relates the force exerted to the distance, 𝑟 , between the objects and to Coulomb’s constant 𝑘 . Which of the following formulas correctly states Coulomb’s law?

  • A 𝐹 = 𝑘 𝑞 𝑞 𝑟
  • B 𝐹 = 𝑞 𝑞 𝑘 𝑟
  • C 𝐹 = 𝑘 𝑞 𝑞 2 𝑟
  • D 𝐹 = 𝑘 𝑞 𝑞 𝑟

Q3:

An object with a charge of 1.50 C and a second charged object that is 0.125 m away exert a force of 2 . 5 6 × 1 0 N on each other. Find the charge on the second charged object. Use 8 . 9 8 8 × 1 0 N⋅m2/C2 for the value of Coulomb’s constant. Answer to three significant figures.

Q4:

Two positively charged spheres are separated by a distance of 8.5 mm, as shown in the diagram. One sphere has a 20 mC charge and the other has a 10 mC charge. The sphere with the 10 mC charge has a force 𝐹 exerted on it. Find 𝐹 . Use 8 . 9 8 8 × 1 0 N⋅m2/C for the value of Coulomb’s constant. Give your answer to two significant figures.

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

Q5:

An object with a charge 𝑞 attracts two other objects that have the charges 𝑞 and 𝑞 , as shown in the diagram. The force 𝐹 that 𝑞 exerts on 𝑞 is twice the force 𝐹 that 𝑞 exerts on 𝑞 . The distance from 𝑞 to 𝑞 is 752 µm and the distance from 𝑞 to 𝑞 is 342 μm. If 𝑞 = 1 2 m C , find 𝑞 . Give your answer to two significant figures.

Q6:

An object with a charge of 𝑞 = 1 5 0 mC is positioned 8.8 cm directly below an object with a charge of 𝑞 = 7 5 mC, as shown in the diagram. On either side of the negatively charged object, at a distance of 6.3 cm, are objects with the charges 𝑞 = 𝑞 = 2 1 mC. Find the magnitude of the net electrical force acting on the negatively charged object. Use 8 . 9 8 8 × 1 0 N⋅m2/C2 for the value of Coulomb’s constant. Give your answer to two significant figures.

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

Q7:

An object with a negative charge is positioned between two fixed, positively charged objects with the charges 𝑞 = 0 . 2 4 C and 𝑞 = 0 . 5 5 C, as shown in the diagram. Once positioned, the negatively charged object remains at rest. The distance 𝑑 between the negatively charged object and the object closer to it is 2.5 cm. Find 𝑑 . Give your answer to two significant figures.

Q8:

An object with a charge of 0.0550 C and a second object that has a charge of 0.110 C exert a force of 3 . 3 3 × 1 0 N on each other. Find the distance between the objects. Use 8 . 9 8 8 × 1 0 N⋅m2/C2 for the value of Coulomb’s constant. Give your answer to three significant figures.

  • A 0.150 m
  • B 0.172 m
  • C 0.0224 m
  • D 0.00163 m
  • E 0.0404 m

Q9:

An object with a charge of 𝑞 = 1 2 mC is positioned 1.5 mm directly above an object with a charge of 𝑞 = 3 2 mC, as shown in the diagram. On either side of the positively charged object, there is another object; each of these objects is 2.5 mm away and each with a charge of 𝑞 = 𝑞 = 4 5 mC. Find the magnitude of the net electrical force on the negatively charged object. Use 8 . 9 8 8 × 1 0 N⋅m2/C2 for the value of Coulomb’s constant. Give your answer to two significant figures.

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

Q10:

Two positively charged spheres are separated by a distance of 3.2 mm, as shown in the diagram. One sphere has double the charge of the other sphere. The sphere with the smaller charge has a force of 24 mN exerted on it. Find the charge of the less charged sphere. Use 8 . 9 8 8 × 1 0 N⋅m2⋅C−2 for the value of Coulomb’s constant. Give your answer to two significant figures.

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