Electric Field Calculator
Calculate electric field strength using E = F/q, Coulomb's law for point charges, or field between parallel plates. Full step-by-step working shown.
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Electric Field Reference Values
| Situation | E (V/m) |
|---|---|
| Earth's fair-weather surface field | ~100 V/m (downward) |
| Thunderstorm cloud base | 10,000–50,000 V/m |
| Air dielectric breakdown | ~3 × 10⁶ V/m |
| 1 µC charge at 1 m | 8,990 V/m |
| Typical capacitor (10 V, 1 mm) | 10,000 V/m |
| X-ray tube anode field | ~10⁸ V/m |
| Atomic field at Bohr radius | ~5.1 × 10¹¹ V/m |
Frequently Asked Questions
Electric field strength E is defined as the force F experienced by a small positive test charge q placed at that point: E = F ÷ q. The units are Newtons per Coulomb (N/C) or equivalently Volts per meter (V/m). For a point charge Q at distance r: E = kQ/r², where k = 8.99 × 10⁹ N·m²/C².
Coulomb's law gives the electrostatic force between two point charges: F = k × |q₁ × q₂| ÷ r². Where k = 8.99×10⁹ N·m²/C², q₁ and q₂ are the charges in Coulombs, and r is the distance in meters. Like charges repel; opposite charges attract. The force decreases with the square of distance.
For a uniform electric field between two parallel plates: E = V ÷ d, where V is the potential difference (voltage) in Volts and d is the plate separation in meters. This produces a uniform field pointing from the positive plate to the negative plate. The field is approximately uniform when the plate dimensions are large compared to the separation.
Electric field is measured in Newtons per Coulomb (N/C) or equivalently Volts per meter (V/m). Both are identical units: 1 N/C = 1 V/m. The Earth's fair-weather electric field at the surface is about 100 V/m pointing downward. Breakdown of air occurs at about 3 × 10⁶ V/m (3 MV/m).
Key Electric Field Formulas
Definition: E = F ÷ q — the force per unit charge at a point in space.
Point charge: E = kQ ÷ r² = Q ÷ (4πε₀r²), where k = 8.99 × 10⁹ N·m²/C² and ε₀ = 8.85 × 10⁻¹² F/m.
Parallel plates: E = V ÷ d (uniform field approximation).
Electric potential: V = kQ ÷ r for a point charge. The relationship E = −dV/dr means E points in the direction of decreasing potential.
- k = 1/(4πε₀) = 8.9875 × 10⁹ N·m²/C²
- The Coulomb is a very large unit; most practical charges are in µC (10⁻⁶) or nC (10⁻⁹) range
- Superposition principle: total E from multiple charges = vector sum of individual fields