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Coulomb's Law worksheet

Grades 11–12 · CCSS HSA.CED.A.4

Solve each problem and show your work. Round answers to 2 decimal places where needed.

1.
Problem 1.
- Solve for: Distance (r)
- Charge 1 (q₁): 3 µC
- Charge 2 (q₂): -3 µC
- Size of the force (|F|): 19 N
- Show distance in: Meters (m)
Find: Distance between charges
Answer
2.
Problem 2.
- Solve for: Force (F)
- Charge 1 (q₁): 2 µC
- Charge 2 (q₂): -2 µC
- Distance between the charges (r): 5 cm
- Show force in: Kilonewtons (kN)
Find: Electric force (magnitude)
Answer
3.
Problem 3.
- Solve for: Distance (r)
- Charge 1 (q₁): 2 µC
- Charge 2 (q₂): -4 µC
- Size of the force (|F|): 17 N
- Show distance in: Nanometers (nm)
Find: Distance between charges
Answer
4.
Problem 4.
- Solve for: Force (F)
- Charge 1 (q₁): 2 µC
- Charge 2 (q₂): -3 µC
- Distance between the charges (r): 5 cm
- Show force in: Dynes (dyn)
Find: Electric force (magnitude)
Answer
5.
Problem 5.
- Solve for: Second charge (q₂)
- Charge 1 (q₁): 4 µC
- Distance between the charges (r): 5 cm
- Size of the force (|F|): 27 N
- The charges: Repel
- Show charge in: Picocoulombs (pC)
Find: Second charge (q₂)
Answer
6.
Problem 6.
- Solve for: Second charge (q₂)
- Charge 1 (q₁): 2 µC
- Distance between the charges (r): 5 cm
- Size of the force (|F|): 20 N
- The charges: Repel
- Show charge in: Coulombs (C)
Find: Second charge (q₂)
Answer
7.
Problem 7.
- Solve for: Force (F)
- Charge 1 (q₁): 2 µC
- Charge 2 (q₂): -3 µC
- Distance between the charges (r): 3 cm
- Show force in: Kilonewtons (kN)
Find: Electric force (magnitude)
Answer
8.
Problem 8.
- Solve for: Distance (r)
- Charge 1 (q₁): 2 µC
- Charge 2 (q₂): -4 µC
- Size of the force (|F|): 12 N
- Show distance in: Centimeters (cm)
Find: Distance between charges
Answer
9.
Problem 9.
- Solve for: Force (F)
- Charge 1 (q₁): 2 µC
- Charge 2 (q₂): -3 µC
- Distance between the charges (r): 4 cm
- Show force in: Dynes (dyn)
Find: Electric force (magnitude)
Answer
10.
Problem 10.
- Solve for: Second charge (q₂)
- Charge 1 (q₁): 3 µC
- Distance between the charges (r): 4 cm
- Size of the force (|F|): 26 N
- The charges: Attract
- Show charge in: Elementary charges (e)
Find: Second charge (q₂)
Answer

Answer key: Coulomb's Law worksheet

1. Distance between charges: 0.07 m
1. Change charge 1 to C, the standard unit the formula uses (1 µC = 0.000001 C)
  $3 µC \times 0.000001$ $= 0.000003 C$
2. Change charge 2 to C, the standard unit the formula uses (1 µC = 0.000001 C)
  $−3 µC \times 0.000001$ $= −0.000003 C$
3. Rearrange Coulomb's law to get the distance r on its own. It ends up under a square root
  $\sqrt{\frac{8,987,551,786.170797 \times 9e-12}{19}}$ $= 0.0652476925 m$
2. Electric force (magnitude): 0.01 kN
1. Change charge 1 to C, the standard unit the formula uses (1 µC = 0.000001 C)
  $2 µC \times 0.000001$ $= 0.000002 C$
2. Change charge 2 to C, the standard unit the formula uses (1 µC = 0.000001 C)
  $−2 µC \times 0.000001$ $= −0.000002 C$
3. Change distance to m, the standard unit the formula uses (1 cm = 0.01 m)
  $5 cm \times 0.01$ $= 0.05 m$
4. Use Coulomb's law: multiply the charges and k, then divide by the distance squared
  $\frac{8,987,551,786.170797 \times 4e-12}{{0.05}^{2}}$ $= 14.3800828579 N$
5. Change the answer to kN, the unit you picked: divide by 1,000
  $\frac{14.380083}{1,000}$ $= 0.01438 kN$
3. Distance between charges: 65,034,115.16 nm
1. Change charge 1 to C, the standard unit the formula uses (1 µC = 0.000001 C)
  $2 µC \times 0.000001$ $= 0.000002 C$
2. Change charge 2 to C, the standard unit the formula uses (1 µC = 0.000001 C)
  $−4 µC \times 0.000001$ $= −0.000004 C$
3. Rearrange Coulomb's law to get the distance r on its own. It ends up under a square root
  $\sqrt{\frac{8,987,551,786.170797 \times 8e-12}{17}}$ $= 0.0650341152 m$
4. Change the answer to nm, the unit you picked: divide by 0.000000001
  $\frac{0.065034}{0.000000001}$ $= 65,034,115.160188 nm$
4. Electric force (magnitude): 2,157,012.43 dyn
1. Change charge 1 to C, the standard unit the formula uses (1 µC = 0.000001 C)
  $2 µC \times 0.000001$ $= 0.000002 C$
2. Change charge 2 to C, the standard unit the formula uses (1 µC = 0.000001 C)
  $−3 µC \times 0.000001$ $= −0.000003 C$
3. Change distance to m, the standard unit the formula uses (1 cm = 0.01 m)
  $5 cm \times 0.01$ $= 0.05 m$
4. Use Coulomb's law: multiply the charges and k, then divide by the distance squared
  $\frac{8,987,551,786.170797 \times 6e-12}{{0.05}^{2}}$ $= 21.5701242868 N$
5. Change the answer to dyn, the unit you picked: divide by 0.00001
  $\frac{21.570124}{0.00001}$ $= 2,157,012.428681 dyn$
5. Second charge (q₂): 1,877,596.97 pC
1. Change charge 1 to C, the standard unit the formula uses (1 µC = 0.000001 C)
  $4 µC \times 0.000001$ $= 0.000004 C$
2. Change distance to m, the standard unit the formula uses (1 cm = 0.01 m)
  $5 cm \times 0.01$ $= 0.05 m$
3. Rearrange Coulomb's law to get the size of the second charge q₂ on its own
  $\frac{27 \times {0.05}^{2}}{8,987,551,786.170797 \times 0.000004}$ $= 0.0000018776 C$
4. The charges repel, so q₂ has the same sign as q₁; convert to pC
  $\frac{0.0000018776}{0.000000000001}$ $= 1,877,596.9698406267 pC$
6. Second charge (q₂): 2.78e-6 C
1. Change charge 1 to C, the standard unit the formula uses (1 µC = 0.000001 C)
  $2 µC \times 0.000001$ $= 0.000002 C$
2. Change distance to m, the standard unit the formula uses (1 cm = 0.01 m)
  $5 cm \times 0.01$ $= 0.05 m$
3. Rearrange Coulomb's law to get the size of the second charge q₂ on its own
  $\frac{20 \times {0.05}^{2}}{8,987,551,786.170797 \times 0.000002}$ $= 0.0000027816 C$
4. The charges repel, so q₂ has the same sign as q₁
  $\frac{0.0000027816}{1}$ $= 0.0000027816 C$
7. Electric force (magnitude): 0.06 kN
1. Change charge 1 to C, the standard unit the formula uses (1 µC = 0.000001 C)
  $2 µC \times 0.000001$ $= 0.000002 C$
2. Change charge 2 to C, the standard unit the formula uses (1 µC = 0.000001 C)
  $−3 µC \times 0.000001$ $= −0.000003 C$
3. Change distance to m, the standard unit the formula uses (1 cm = 0.01 m)
  $3 cm \times 0.01$ $= 0.03 m$
4. Use Coulomb's law: multiply the charges and k, then divide by the distance squared
  $\frac{8,987,551,786.170797 \times 6e-12}{{0.03}^{2}}$ $= 59.9170119078 N$
5. Change the answer to kN, the unit you picked: divide by 1,000
  $\frac{59.917012}{1,000}$ $= 0.059917 kN$
8. Distance between charges: 7.74 cm
1. Change charge 1 to C, the standard unit the formula uses (1 µC = 0.000001 C)
  $2 µC \times 0.000001$ $= 0.000002 C$
2. Change charge 2 to C, the standard unit the formula uses (1 µC = 0.000001 C)
  $−4 µC \times 0.000001$ $= −0.000004 C$
3. Rearrange Coulomb's law to get the distance r on its own. It ends up under a square root
  $\sqrt{\frac{8,987,551,786.170797 \times 8e-12}{12}}$ $= 0.0774060798 m$
4. Change the answer to cm, the unit you picked: divide by 0.01
  $\frac{0.077406}{0.01}$ $= 7.740608 cm$
9. Electric force (magnitude): 3,370,331.92 dyn
1. Change charge 1 to C, the standard unit the formula uses (1 µC = 0.000001 C)
  $2 µC \times 0.000001$ $= 0.000002 C$
2. Change charge 2 to C, the standard unit the formula uses (1 µC = 0.000001 C)
  $−3 µC \times 0.000001$ $= −0.000003 C$
3. Change distance to m, the standard unit the formula uses (1 cm = 0.01 m)
  $4 cm \times 0.01$ $= 0.04 m$
4. Use Coulomb's law: multiply the charges and k, then divide by the distance squared
  $\frac{8,987,551,786.170797 \times 6e-12}{{0.04}^{2}}$ $= 33.7033191981 N$
5. Change the answer to dyn, the unit you picked: divide by 0.00001
  $\frac{33.703319}{0.00001}$ $= 3,370,331.919814 dyn$
10. Second charge (q₂): -9,629,866,719,176.63 e
1. Change charge 1 to C, the standard unit the formula uses (1 µC = 0.000001 C)
  $3 µC \times 0.000001$ $= 0.000003 C$
2. Change distance to m, the standard unit the formula uses (1 cm = 0.01 m)
  $4 cm \times 0.01$ $= 0.04 m$
3. Rearrange Coulomb's law to get the size of the second charge q₂ on its own
  $\frac{26 \times {0.04}^{2}}{8,987,551,786.170797 \times 0.000003}$ $= 0.0000015429 C$
4. The charges attract, so q₂ has the opposite sign to q₁; convert to e
  $\frac{−0.0000015429}{1.602176634e-19}$ $= −9,629,866,719,176.625 e$