Electric Force Between Point Charges (Copy)

• Electric force is the force of attraction or repulsion between two electrically charged particles.
• The electric force between two point charges in a vacuum or air is governed by Coulomb’s Law.

Coulomb’s Law:

• Coulomb’s Law describes the magnitude of the electrostatic force between two stationary point charges:
  • F = Q₁Q₂ / (4πε₀r²)

  Where:
  F = magnitude of the force (N)
  Q₁ and Q₂ = charges (C)
  r = distance between the charges (m)
  ε₀ = permittivity of free space = 8.85 × 10⁻¹² C² N⁻¹ m⁻²

• The direction of the force:
  • Repulsive if charges are like (both positive or both negative)
  • Attractive if charges are unlike (positive and negative)

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change A2 Level Physics Full Scale Course

Assumption for Spherical Conductors

• For a point outside a uniformly charged spherical conductor, the entire charge can be treated as if it were concentrated at the centre of the sphere.
• This is valid due to spherical symmetry.
• Hence, Coulomb’s Law can be used for:
  • Two point charges
  • A point charge and a spherically symmetric charged sphere (from outside the sphere)

Vector Nature of Electric Force

• The electric force is a vector quantity:
  • Acts along the line joining the two charges
  • The net force on a charge due to multiple other charges is found using vector addition of all individual forces

• Example:
  Two charges Q₁ = +2.0 × 10⁻⁶ C and Q₂ = –3.0 × 10⁻⁶ C are placed 0.50 m apart in vacuum.
  Find the force between them:

  F = (2.0 × 10⁻⁶)(3.0 × 10⁻⁶) / (4π × 8.85 × 10⁻¹² × 0.5²)
  F ≈ 0.216 N (attractive)

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change A2 Level Physics Full Scale Course

Comparison with Newton’s Law of Gravitation

Units

• Force (F): Newtons (N)
• Charge (Q): Coulombs (C)
• Distance (r): Metres (m)
• Permittivity (ε₀): C² N⁻¹ m⁻²

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change A2 Level Physics Full Scale Course

Vector Calculations Example:

• If two forces F₁ and F₂ act at an angle, the resultant force F is calculated using vector methods:
  • F² = F₁² + F₂² + 2F₁F₂cosθ
  • Useful in multi-charge systems (e.g. charges at triangle corners)

Graphical Analysis:

• Force vs. distance graph:
  • Shape: Inverse square law
  • As distance r increases, force decreases rapidly
  • At very small r, force becomes very large

• The use of Coulomb’s law is essential for:
  • Understanding atomic and molecular structure
  • Predicting interactions in particle physics
  • Engineering applications like capacitors and insulators

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change A2 Level Physics Full Scale Course