Electrostatic force (Coulomb force) is a fundamental force that acts between electric charges. Let us understand Coulomb’s law, which provides its quantitative description.
Basic Knowledge
Electric charge (electric charge) has two types, positive (+) and negative (−). Like charges repel, while opposite charges attract. The unit of charge is the coulomb [C].
The charge of one electron is e = 1.6 × 10⁻¹⁹ C (the elementary charge), and charge is always an integral multiple of the elementary charge (quantization of charge).
Coulomb’s law: When charges q₁ and q₂ are separated by distance r,F = k q₁q₂ / r²
Here, k = 9.0 × 10⁹ N·m²/C² (Coulomb constant). F > 0 indicates repulsion, and F < 0 indicates attraction.
Using the permittivity of free space ε₀, k = 1/(4πε₀), where ε₀ = 8.85 × 10⁻¹² C²/(N·m²).
Electric charge (charge) (The source of electrical properties. Unit: C)
Elementary charge e (The absolute value of the charge of an electron or proton. 1.6 × 10⁻¹⁹ C)
Coulomb constant k (9.0 × 10⁹ N·m²/C². k = 1/(4πε₀))
Permittivity ε₀ (Permittivity of free space. 8.85 × 10⁻¹² C²/(N·m²))
Law of conservation of charge (The total amount of charge does not change in an isolated system)
Quantization of charge (Charge can take only integral multiples of the elementary charge)
Further Study (Background and Significance)
Coulomb’s law has the same inverse-square form as the law of universal gravitation F = Gm₁m₂/r². However, electric force is approximately 10³⁶ times stronger than gravity, and shielding occurs because both positive and negative charges exist. This is why electric force does not dominate on the scale of everyday life.
In conductors, free electrons move and electrostatic induction occurs. In insulators (dielectrics), dielectric polarization occurs. When a conductor is grounded (earthed), its electric potential is fixed at zero.
The conservation and quantization of charge are foundations of modern physics, and the elementary charge was precisely measured in Millikan’s oil-drop experiment (1909).
- Coulomb’s law: F = kq₁q₂/r² (inversely proportional to r²)
- k = 9.0 × 10⁹ N·m²/C²
- Like charges → repulsion, opposite charges → attraction
- Elementary charge e = 1.6 × 10⁻¹⁹ C
- Conservation and quantization of charge are universal
- It is an inverse-square law like gravity, but vastly stronger
- k = 1/(4πε₀)
Points to Note (Easily Confused)
① F is the magnitude of force (a scalar). Determine its direction from the signs. ② r is a distance, not a position coordinate. ③ When the medium is not a vacuum or air, k must be divided by ε (k → k/ε_r). ④ The analogy with gravity is useful, but electric force is fundamentally different because it can also be repulsive.
Practice
- Find the magnitude of the Coulomb force when charges of 2.0 × 10⁻⁶ C and 3.0 × 10⁻⁶ C are 1.0 m apart.
- If the elementary charge is e, what is the charge of a proton in C? What about an electron?
- Write the relationship between the Coulomb constant k and the permittivity of free space ε₀.