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Definition

Coulomb's law is a law that explains the releationship between 2 or more electrical charges.

This law states that: "The magnitude, or absolute value, of the attractive or repulsive electrostatic force between two point charges is directly proportional to the product of the magnitudes of their charges and inversely proportional to the squared distance between them."[1]

Formula

F = k Q1 × Q2⁄r2

where,

Unit Conversions (for Coulomb)

  1. n mC (milliCoulomb) = n * 10-3 C
  2. n MC (MicroCoulomb) = n * 10-6 C (Alternative form: μC)
  3. n nC (nanoCoulomb) = n * 10-9 C
  4. n Å (Ångström) = n * 10-10 C

Examples & Exercises

    1. Find F.


      Given:

      r = 30 cm = 0,3 m = 3 × 10-1 m
      Q1 = 2 MC = 2 × 10-6
      Q2 = 3 MC = 3 × 10-6

      Solution:

      F = k Q1 × Q2⁄r2
      F = 9 × 1092 × 10-6 ‧ 3 × 10-6⁄(3 × 10-1)2 = 9 × 109 ‧ 2 × 10-6 ‧ 3 × 10-6⁄9 × 10-2
      = 109 ‧ 2 × 10-6 ‧ 3 × 10-6⁄10-2 = 10-3 × 6⁄10-2
      = 6 × 10-1

    2. Find F.


      Given:

      r=30 cm=0,3 m=3×10−1r2=(3×10−1)2=9×10−2Q1=6 MCQ2=12 MC \begin{aligned} r &= 30 \textnormal{ cm} = 0,3 \textnormal{ m} = 3 \times 10^{-1}\\ r^2 &= (3 \times 10^{-1})^2 = 9 \times 10^{-2}\\ Q_1 &= 6 \textnormal{ MC}\\ Q_2 &= 12 \textnormal{ MC} \end{aligned}

      Solution:

      F=kQ1Q2r2=9×1096×10−6⋅12×10−69×10−2=109⋅6×10−6⋅12×10−610−2=6⋅12⋅109⋅10−6⋅10−610−2=72⋅10−310−2=72×10−1 \begin{aligned} F &= k\dfrac{Q_1Q_2}{r^2}\\ &= 9 \times 10^9\dfrac{6 \times 10^{-6} \cdot 12 \times 10^{-6}}{9 \times 10^{-2}}\\ &= \dfrac{10^9 \cdot 6 \times 10^{-6} \cdot 12 \times 10^{-6}}{10^{-2}} = \dfrac{6 \cdot 12 \cdot 10^9 \cdot 10^{-6} \cdot 10^{-6}}{10^{-2}}\\ &= \dfrac{72 \cdot 10^{-3}}{10^{-2}}\\ &= 72 \times 10^{-1} \end{aligned}

    3. If F = 9 × 109, Find r.


      Given:

      Q1=4 mCQ2=4 mCF=9×109 N \begin{aligned} Q_1 &= 4 \textnormal{ mC}\\ Q_2 &= 4 \textnormal{ mC}\\ F &= 9 \times 10^9 \textnormal{ N} \end{aligned}

      Solution:

      F=kQ1Q2r29×109=9×1094×10−3⋅4×10−3r29×109r2=9×109⋅4×10−3⋅4×10−3r2=4×10−3⋅4×10−3=16×10−6r=16×10−6=4×10−3 \begin{aligned} F &= k\dfrac{Q_1Q_2}{r^2}\\ 9 \times 10^9 &= 9 \times 10^9\dfrac{4 \times 10^{-3} \cdot 4 \times 10^{-3}}{r^2}\\ 9 \times 10^9 r^2 &= 9 \times 10^9 \cdot 4 \times 10^{-3} \cdot 4 \times 10^{-3}\\ r^2 &= 4 \times 10^{-3} \cdot 4 \times 10^{-3}\\ &= 16 \times 10^{-6}\\ r &= \sqrt{16 \times 10^{-6}}\\ &= 4 \times 10^{-3} \end{aligned}

    References

    1. Coulomb, 1785. "Second mémoire sur l'électricité et le magnétisme"