Physics Chapter: Coulomb's Law

Coulomb's Law

• There are two types of electric charges: positive and negative.
• Like charges repel each other, while unlike charges have mutual attraction.
• The magnitude of the electric force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
• The mathematical form of Coulomb's law is: F = kq₁q₂/r², where k is a constant.
• In S.I. units, k is written as 1/4πε₀, where ε₀ is the permittivity of free space.
• The value of ε₀ is 8.85 x 10⁻¹² C²/N-m² and that of 1/4πε₀ is 8.99 x 10⁹ N-m²/C or 9 x 10⁹ N-m²/C.

Vector Form of Coulomb's Law

• The force F experienced by a point charge q₂ situated at a vector distance r from a point charge q₁ at the origin O is given by: F = (1/4πε₀) q₁q₂/r² * r̂.
• The magnitude of each force is F = (1/4πε₀) q₁q₂/r².

Unit of Charge

• In S.I. system, the unit of charge is coulomb (C) and is defined as the amount of charge that flows through a cross-section of a wire in 1 second if there is a steady current of 1 ampere in the wire.
• 1 coulomb (C) = 1 ampere-second (A-s).
• An alternative definition of coulomb is: the amount of charge which when placed at a distance of 1 m from an equal and similar charge in vacuum, repels it with a force of 9 x 10⁹ newton.
• The most fundamental unit of charge is the magnitude of charge on an electron or proton, denoted by e.

Electromagnetics

• The charge on an electron is -e and that on a proton is +e, with e being a fundamental unit of charge that is very small.
• A Coulomb represents the negative of the total charge of about 6 × 10^18 electrons, equivalent to a current of 1 ampere.
• Typical values of charge range from about 10^(-6) C to 10^6 C, making microcoulomb (µC) and nanocoulomb (nC) units useful in measurements.
• 1 microcoulomb (1 µC) = 10^(-6) C and 1 nanocoulomb (1 nC) = 10^(-9) C.

Importance of Coulomb's Law

• Coulomb's law applies to point charges, but can be extended to distributions of charges.
• The law holds good over a wide range of distances, from 10^(-15) m to several kilometers.
• Coulomb's law, combined with quantum theory, explains forces that bind:
  • Electrons with the nucleus in an atom.
  • Atoms to form a molecule.
  • A large number of atoms or molecules to form liquids and solids.
• The atomic nucleus, containing positively charged protons and uncharged neutrons, has a size of about 10^(-15) m.
• Coulomb's law cannot account for the stability of an atomic nucleus due to the presence of nuclear forces.
• Nuclear forces are weaker than the Coulomb force at separations of more than approximately 10^(-15) m, but stronger at separations of 10^(-15) m or less.

Quantization of Charge

• Experimentally, the charge on an object is always an integral multiple of the charge of an electron (1.6 × 10^(-19) C), i.e., q = ne, where n = 1, 2, 3, ... .
• This property of charge is called quantization of charge, with e being the smallest unit of charge and called the elementary charge.
• Charge is additive, meaning the total charge on a body is the algebraic sum of the charges at different parts of the body.

Conservation of Charge

• The total amount of charge in an isolated system is always constant.
• Charge may be transferred within the system, but the net charge remains the same.
• Charge cannot be created or destroyed, following the law of conservation of charge.
• Examples supporting this law include the transfer of charge when rubbing a glass rod with silk.