Charges interact via Coulomb’s law F = k q₁ q₂ / r², producing an electric field E (vector, N/C) and potential V (scalar, J/C). Superposition lets you sum contributions from multiple charges or continuous distributions. Gauss’s law ∮ E·dA = Q_enclosed / ε₀ simplifies symmetric cases. Capacitors store energy with U = ½ C V² and effective capacitance depends on geometry and series/parallel combinations.
Electrostatics calculators
Point charges, continuous fields, potentials, and capacitors
📈 Electrostatics graph
Basic electrostatics constants & quantities
| Quantity | Symbol / Value | SI unit | Notes |
|---|---|---|---|
| Electric charge | q, Q; e = 1.602×10⁻¹⁹ C | C | Charge is quantized in multiples of e |
| Coulomb’s constant | k = 1/(4πε₀) ≈ 9×10⁹ | N·m²/C² | Often use k ≈ 9×10⁹ N·m²/C² |
| Permittivity of free space | ε₀ = 8.854×10⁻¹² | F/m | Relates E, D fields; k = 1/(4πε₀) |
| Electric field | E | N/C or V/m | Vector; E = F/q (test charge) |
| Electric potential | V | V (J/C) | Scalar; work per unit charge |
Fields, Gauss’s law, potential & capacitors
| Concept | Formula | Notes |
|---|---|---|
| Coulomb’s law (magnitude) | F = k q₁ q₂ / r² | Along the line joining charges |
| Electric field (point charge) | E = k q / r² | Direction: away from +q, toward −q |
| Superposition | E_total = ΣEᵢ, V_total = ΣVᵢ | Vector sum for E, scalar sum for V |
| Gauss’s law | ∮ E·dA = Q_enclosed / ε₀ | Use high symmetry: sphere, cylinder, plane |
| Infinite line charge | E = λ / (2πε₀ r) | r = perpendicular distance |
| Infinite sheet | E = σ / (2ε₀) | Uniform sheet; independent of distance |
| Two sheets (±σ) | E_between = σ / ε₀ | Field doubles between, cancels outside |
| Sphere (outside) | E = kQ/r², V = kQ/r | Acts like point charge at center |
| Solid sphere (inside) | E = kQr/R³ | Uniform volume charge |
| Potential energy of two charges | U = k q₁ q₂ / r | Positive for like charges (repulsive) |
| Capacitance (parallel plate) | C = ε₀ A / d, with dielectric C = κ ε₀ A / d | κ > 1 for dielectric |
| Energy stored in capacitor | U = ½ C V² = ½ QV = ½ Q² / C | Energy density u = ½ ε₀ E² (vacuum) |
| Series capacitors | 1/C_eq = Σ (1/Cᵢ) | Same charge, voltages add |
| Parallel capacitors | C_eq = ΣCᵢ | Same voltage, charges add |
About this electrostatics tool
This page groups the main school/JEE/NEET electrostatics formulas in one place: force between point charges, electric field and potential, Gauss’s law shortcuts for symmetric distributions, and capacitor formulas including dielectrics and series/parallel combinations. Each calculator is paired with step-by-step reasoning so you can see which formula is used and how the numbers are substituted.