Point Charge — Definition, Electric Field and Potential

A point charge is a theoretical concept in which: • All electric charge of a body is assumed to be concentrated at a single mathematical point (having no physical dimensions) • The body is treated as if it has zero size • This approximation is valid when the distance between objects is much larger than their actual size

Symbol: q (in coulombs, C) SI unit of charge: Coulomb (C)

Physical meaning: • An electron, proton, or ion can be approximated as point charges at large distances • Planets and stars can be treated as point masses (analogous concept)

The electrostatic force between two point charges q₁ and q₂ separated by distance r:

F = k × q₁ × q₂ / r²

Where: • F = electrostatic force (in Newtons, N) • k = Coulomb's constant = 9 × 10⁹ N·m²·C⁻² • q₁, q₂ = magnitudes of point charges (in Coulombs, C) • r = distance between the charges (in metres, m)

Also written as: F = q₁q₂ / (4πε₀r²) Where ε₀ = 8.854 × 10⁻¹² C²/N·m² (permittivity of free space) k = 1/(4πε₀) = 9 × 10⁹ N·m²/C²

Direction: • Like charges (same sign): Repulsive force • Unlike charges (opposite sign): Attractive force

Electric field (E) at distance r from a point charge q:

E = kq / r² Or: E = q / (4πε₀r²)

• E is in N/C or V/m • E is directed radially outward from positive charge • E is directed radially inward toward negative charge • E is inversely proportional to r² (follows inverse square law)

Electric potential (V) at distance r from a point charge q:

V = kq / r Or: V = q / (4πε₀r)

• V is in Volts (V) or J/C • V is a scalar quantity (unlike E which is a vector) • V is positive for positive charge, negative for negative charge • V approaches zero as r → ∞ • Potential energy: U = qV = kq₁q₂/r

Key comparison: • Electric field E ∝ 1/r² (inverse square) • Electric potential V ∝ 1/r (inverse first power)