Coulomb's Law Physics Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

hard
Two identical charges experience a force of 0.1ย N0.1 \text{ N} when separated by 0.3ย m0.3 \text{ m}. What is the magnitude of each charge?

Solution

  1. 1
    Since the charges are identical, q1=q2=qq_1 = q_2 = q. Coulomb's law: F=kq2r2F = k\frac{q^2}{r^2}.
  2. 2
    Solve for qq: q=Fr2k=0.1ร—0.099ร—109q = \sqrt{\frac{Fr^2}{k}} = \sqrt{\frac{0.1 \times 0.09}{9 \times 10^9}}
  3. 3
    q=0.0099ร—109=10โˆ’12=10โˆ’6ย C=1ย ฮผCq = \sqrt{\frac{0.009}{9 \times 10^9}} = \sqrt{10^{-12}} = 10^{-6} \text{ C} = 1 \text{ } \mu\text{C}

Answer

q=1ย ฮผCq = 1 \text{ } \mu\text{C}
By rearranging Coulomb's law, we can find unknown charges from measured forces and distances. The symmetry of identical charges simplifies the algebra.

About Coulomb's Law

Coulomb's law gives the electric force between two point charges. The force gets larger when the charges are larger and gets smaller with the square.

Learn more about Coulomb's Law โ†’

More Coulomb's Law Examples

Example 1 medium

Two charges [formula] and [formula] are separated by [formula]. What is the electrostatic force betw

Example 3 medium

If the distance between two charges is tripled, by what factor does the electrostatic force change?

Example 4 hard

Two charges [formula] and [formula] are separated by [formula]. (a) Calculate the force between them

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