Coulomb's Law
Coulomb's Law states that the magnitude of the electrostatic force between two point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them, with the force acting along the line joining the charges. Formulated by Charles-Augustin de Coulomb in 1785 through careful torsion balance experiments, it is the electrostatic analogue of Newton's Law of Universal Gravitation and forms the cornerstone of classical electrostatics. The law governs the forces responsible for atomic bonding, molecular structure, and the operation of capacitors and electrostatic devices.
Key Formula
F = k × |q₁ × q₂| / r²
LaTeX: F = k_e \frac{|q_1 q_2|}{r^2}
| Symbol | Meaning | Unit |
|---|---|---|
| F | Electrostatic force between charges | N |
| kₑ | Coulomb's constant (8.988 × 10⁹) | N·m²/C² |
| q₁, q₂ | Magnitudes of the two point charges | C |
| r | Distance between the two charges | m |
Worked Example
Problem
Two point charges q₁ = +6 μC and q₂ = −4 μC are placed 0.3 m apart in vacuum. Calculate the magnitude of the electrostatic force between them and state whether it is attractive or repulsive.
Solution
Step 1: Write Coulomb's Law. F = kₑ × |q₁ × q₂| / r² Step 2: Convert units: q₁ = 6 × 10⁻⁶ C, q₂ = 4 × 10⁻⁶ C, r = 0.3 m. F = (8.988 × 10⁹) × (6 × 10⁻⁶ × 4 × 10⁻⁶) / (0.3)² F = (8.988 × 10⁹) × (24 × 10⁻¹²) / 0.09 F = (8.988 × 10⁹ × 2.667 × 10⁻¹⁰) F ≈ 2.397 N Step 3: Since q₁ and q₂ have opposite signs, the force is attractive.
Answer
F ≈ 2.40 N (attractive force)
Comparison: Coulomb's Law vs. Newton's Law of Gravitation
| Property | Coulomb's Law | Newton's Gravitation | Note |
|---|---|---|---|
| Force formula | F = k|q₁q₂|/r² | F = Gm₁m₂/r² | Both inverse-square laws |
| Constant | k = 8.99 × 10⁹ N·m²/C² | G = 6.67 × 10⁻¹¹ N·m²/kg² | Electric force much stronger |
| Nature | Attractive or repulsive | Always attractive | Charge can be ± ; mass always + |
| Acts on | Electric charges | Masses | Different fundamental properties |
| Range | Infinite (in vacuum) | Infinite | Both long-range forces |
Interactive Tools
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Related Terms
Electric Charge
Electric charge is a fundamental intrinsic property of matter that causes particles to experience a force when placed in an electromagnetic field, existing as either positive (carried by protons) or negative (carried by electrons) with an elementary charge unit of e = 1.602 × 10⁻¹⁹ coulombs. Charge is conserved in all physical processes (the total charge of an isolated system remains constant), and it is quantised, meaning any observable charge is an integer multiple of the elementary charge. Electric charge is the source of the electric force, which is described by Coulomb's Law and governs all electromagnetic interactions in nature and technology.
Electric Field
An electric field is a vector field that exists in the region around an electric charge or a changing magnetic field, representing the electrostatic force that would be exerted per unit positive charge placed at any point in space. The field lines emanate outward from positive charges and point inward toward negative charges, with the density of field lines indicating field strength. Electric fields are central to understanding capacitors, electromagnetic waves, semiconductor devices, and the operation of all electrical equipment from simple circuits to complex communication systems.
Electric Potential
Electric potential at a point in space is the amount of electric potential energy per unit positive test charge at that location, representing the work done per unit charge to bring a positive test charge from infinity to that point against the electric field. It is a scalar quantity measured in volts (V), where 1 volt equals 1 joule per coulomb. Electric potential is fundamental to understanding capacitors, batteries, and electrical circuits, and the difference in electric potential between two points (voltage) drives the flow of electric current.
Named after Charles-Augustin de Coulomb (1736–1806), a French military engineer and physicist who formulated the law in 1785 using a torsion balance he invented. "Law" derives from Old English "lagu" (something laid down or fixed).