Electrostatics Essentials: Charge, Coulomb's Law, Electric Fields

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Electrostatics Fundamentals

This document covers key concepts in electrostatics, including properties of electric charge, Coulomb's Law, and electric fields.

Properties of Electric Charge

Here are four fundamental properties of electric charge:

  1. Additivity of Charges: The total charge of a system is the algebraic sum of all individual charges present in the system.
  2. Conservation of Charge: The total charge of an isolated system remains unchanged over time. Charge can neither be created nor destroyed, only transferred.
  3. Quantization of Charge: The total charge of a body is always an integral multiple of a basic quantum of charge, denoted as 'e'. This means charge q can only exist as q = ±ne, where n is an integer (1, 2, 3, ...).
  4. Interaction of Charges: Like charges repel each other, while unlike charges attract each other.

Coulomb's Law in Electrostatics

Statement: 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. This force acts along the line joining the two charges.

Consider two point charges, q₁ and q₂, separated by a distance 'r' in a vacuum. According to Coulomb's Law, the magnitude of the force F between them is given by:

F ∝ |q₁q₂| / r²

To convert this proportionality into an equation, we introduce a proportionality constant K:

F = K * (|q₁q₂| / r²)

Where K is the proportionality constant. In the SI system, for free space (vacuum), K is given by:

K = 1 / (4πε₀)

Here, ε₀ (epsilon naught) is the permittivity of free space, approximately 8.854 × 10⁻¹² C²/(N·m²).

Thus, Coulomb's Law can be written as:

F = (1 / (4πε₀)) * (|q₁q₂| / r²)

Coulomb's Law in Vector Form

The force on charge q₁ due to charge q₂ (denoted as F₁₂) is given by:

F₁₂ = (1 / (4πε₀)) * (q₁q₂ / r₁₂²) * r̂₁₂

Where:

  • r₁₂ is the distance between q₁ and q₂.
  • r̂₁₂ is the unit vector pointing from q₂ to q₁ (along the line joining the charges).
  • ε₀ is the permittivity of free space.

Electric Field Due to a Point Charge

The expression for the electric field E at a point due to a point charge Q at a distance 'r' from the charge in free space is:

E = (1 / (4πε₀)) * (Q / r²)

Where ε₀ is the permittivity of free space.

Drawing Electric Field Lines

Electric field lines are a way to visualize electric fields. They originate from positive charges and terminate on negative charges, never crossing each other. Here are common configurations:

  1. For a positive point charge (q > 0): Field lines radiate outwards from the charge.
  2. For a negative point charge (q < 0): Field lines converge inwards towards the charge.
  3. For a system of two positive charges: Field lines originate from both charges and curve away from each other, indicating repulsion. There is a neutral point between them.
  4. For an electric dipole (one positive and one negative charge): Field lines originate from the positive charge and terminate on the negative charge, forming continuous curves.

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