The foundation of electrical phenomena is electric charge. We study the forces between charges and the electric field produced around them.
Basic Knowledge
Basics of electric charge:
・There are two types: positive charge (+) and negative charge (−)
・Like signs: repel (repulsive force); unlike signs: attract (attractive force)
・Law of conservation of charge: The total amount of charge in an entire system remains constant
・Elementary charge: e = 1.6 × 10⁻¹⁹ C (the magnitude of the charge of one electron)
Coulomb's law: When two point charges Q₁ and Q₂ are separated by a distance r, the electrostatic force is:F = k Q₁Q₂ / r²
・k = 9.0 × 10⁹ N·m²/C² (Coulomb's constant)
・The force is proportional to the product of the charges and inversely proportional to the square of the distance
Electric field E: The magnitude and direction of the electrostatic force acting on a unit positive charge (+1 C) [N/C = V/m]
・Electric field from a point charge Q: E = kQ/r²
・Direction of the electric field: outward from a positive charge and inward toward a negative charge
Electric charge (charge, Q)（the amount of electricity. Unit: C (coulomb)）
Elementary charge (e)（e = 1.6 × 10⁻¹⁹ C. The magnitude of the charge of an electron or proton）
Coulomb's law（F = kQ₁Q₂/r². Electrostatic force is inversely proportional to the square of the distance）
Electric field (electric field, E)（the force acting on a unit positive charge. Unit: N/C or V/m）
Electric field lines（lines representing the direction and strength of an electric field. A denser arrangement indicates a stronger field）
Law of conservation of charge（the total charge in an isolated system does not change）
Further Exploration (Background and Significance)
Coulomb's law has the same form as Newton's law of universal gravitation, F = Gm₁m₂/r². Gravity is always attractive, but electrostatic force can be either attractive or repulsive. Electrostatic force is also overwhelmingly stronger than gravity, and it is what allows electrons to move around atomic nuclei.
An electric field is a field concept that describes “the direction and magnitude of the force experienced by a charge placed at a certain point.” It can be visualized using electric field lines. In a uniform electric field (such as inside a parallel-plate capacitor), electric field lines are parallel and equally spaced.
Electrostatic induction: When an electric field is applied to a conductor, free electrons move and charges become unevenly distributed. When the conductor is grounded, excess charge escapes, and the conductor remains charged even after the charged object is removed (dielectric polarization is also related).
Today, the SI unit of charge, the coulomb (C), is used, but the elementary charge e is discussed as a fundamental unit, and fractions of e (quarks) also exist in particle physics.
- Like charges: repulsive force; unlike charges: attractive force
- Coulomb's law: F = kQ₁Q₂/r²
- k = 9.0 × 10⁹ N·m²/C²
- Electric field E = F/q = kQ/r²
- Electric field lines emerge from positive charges and enter negative charges
- Unit of electric field: N/C = V/m
- Elementary charge e = 1.6 × 10⁻¹⁹ C
Notes (Common Confusions)
① In Coulomb's law, r is the distance squared (r²), not the first power of the distance. ② The electric field E is the force acting on a unit positive charge (+1 C). The actual force is F = qE, and if charge q is negative, its direction is opposite. ③ The density of electric field lines represents the strength of the electric field. They are equally spaced in a uniform field. ④ The electric field inside a conductor is zero (in electrostatic equilibrium). Charge is distributed on the surface.
Practice
- Charges of 2.0 × 10⁻⁶ C and 3.0 × 10⁻⁶ C are 1.0 m apart. Find the Coulomb force (k = 9.0 × 10⁹).
- A charge of −2.0 × 10⁻⁶ C is placed in a region where the electric field is 500 N/C. Find the magnitude of the force acting on the charge.
- From which charge do electric field lines emerge, and into which charge do they enter: positive or negative?