Coulomb's Law
The inverse-square law of electric force.
8 minUpdated Coulomb's lawpermittivity of free space
Lesson at a glanceShow the key points
- F = kq₁q₂/r² = q₁q₂/4πε₀r² (29.1–29.2), along the line joining the charges.
- k = 8.99 × 10⁹ N m² C⁻²; ε₀ = 8.854 × 10⁻¹² C² N⁻¹ m⁻².
- Vector form F⃗ = kq₁q₂ r⃗/r³; forces from several charges add as vectors.
Coulomb measured how the electric force depends on charge and distance. The answer looks just like Newton’s law of gravitation, with charge in place of mass.
The law
Coulomb's law(29.1–29.2)
k = 8.99 × 10⁹ N m² C⁻²; ε₀ = 8.854 × 10⁻¹² C² N⁻¹ m⁻² is the permittivity of free space
The force acts along the line joining the charges: repulsive for like charges, attractive for unlike. In vector form, with r⃗ the position of the charge feeling the force relative to the one exerting it:
Interactive
Coulomb's law
Two point charges push or pull each other along the line joining them, with force kq₁q₂/r². Like charges repel, unlike attract. Halve the distance and the force becomes four times as large; the pair of forces is always equal and opposite.
7.19N
natureattractive
Worked example
Forces on a corner charge
Charges +4.0 µC at A, −2.0 µC at B and +1.0 µC at C sit at the corners of an equilateral triangle of side 6.0 cm. Find the net force on C.
Worked example
Where is the force zero?
+9.0 µC and −1.0 µC are held 30 cm apart. Where can a third charge sit with no net force on it?
What to remember
- 1F = q₁q₂/4πε₀r², along the line joining the charges; like repel, unlike attract.
- 2k = 1/4πε₀ ≈ 9 × 10⁹ N m² C⁻².
- 3Forces from several charges add as vectors.
Check yourself
Q1
The distance between two charges is tripled. The force becomes…
Q2
Each of two charges is doubled and the distance doubled. The force…
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