Physics

Electrostatics

Coulomb force, electric field, potential, and a Gauss-law sketch.

Basics

Coulomb’s law

The force between two point charges scales with the product of the charges and as 1/r². Likes repel; unlikes attract. The constant is k = 1/(4πε₀). With several charges, add forces as vectors. This page stays with charges at rest. Moving charges and magnetism belong elsewhere in the handbook.

Electric field

Electric field E is the force on a test charge q₀ divided by q₀. For a point charge, E = k q / r², outward for + and inward for −. Field lines leave + and enter − and do not cross. In a uniform field, F = q E is constant. Inside a conductor in electrostatics, E=0 and excess charge sits on the surface.

Potential and potential energy

Potential V is potential energy per unit charge. In a uniform field, ΔV = −E Δs (potential falls when you walk with the field). For a point charge, V = k q / r with V=0 at infinity. Potential energy is U = q V. Voltage is a potential difference. On an equipotential, moving without work leaves U unchanged. E points opposite the gradient of V.

Gauss-law sketch

The electric flux out of a closed surface equals the enclosed charge over ε₀: Φ_E = Q_encl / ε₀. With high symmetry (sphere, infinite plane, infinite line) you can read |E| off the face. The Gaussian surface is a calculation fiction. Without symmetry, use superposition or numerics. This sketch is one static Maxwell equation.

Formulas

Coulomb force

F = k |q₁ q₂| / r², k = 1/(4π ε₀)

Magnitude; sign sets direction.

Symbols

r separation
ε₀ vacuum permittivity

Point-charge field

E = k q / r²

Outward for positive q.

Symbols

E field magnitude

Point-charge potential

V = k q / r, U = q V

V=0 at infinity. U is energy of charge q.

Symbols

V electric potential

Gauss’s law

∮ E · dA = Q_encl / ε₀

Closed surface; symmetry unlocks |E|.

Symbols

Q_encl enclosed charge

Key table

k	about 8.99×10⁹ N·m²/C²
Conductor surface	in electrostatics E is normal to the surface; sharper tips are stronger
Superposition	add fields, potentials, and forces (linear)