Electric Field Calculator

Calculate electric field strength using force and charge or from a point charge. Essential for electrostatics, electromagnetic theory, and physics problems.

**Method 1: Field from Force** E = F / q Where: • E = Electric field strength (N/C or V/m) • F = Electric force on test charge (N) • q = Test charge magnitude (C) **Method 2: Field from Point Charge** E = k × Q / r² Where: • E = Electric field strength (N/C or V/m) • k = Coulomb's constant = 8.99×10⁹ N·m²/C² • Q = Source charge magnitude (C) • r = Distance from source charge (m) **Unit Equivalence:** 1 N/C = 1 V/m **Electric Potential:** V = k × Q / r (volts) E = -dV/dr (field is potential gradient) **Common Charge Values:** • Elementary charge e = 1.602×10⁻¹⁹ C • 1 nanocoulomb (nC) = 10⁻⁹ C • 1 microcoulomb (μC) = 10⁻⁶ C
**Example 1 (Force Method):** An electron (q = 1.6×10⁻¹⁹ C) experiences 3.2×10⁻¹⁵ N force. • Force = 3.2×10⁻¹⁵ N • Test charge = 1.6×10⁻¹⁹ C • E = 3.2×10⁻¹⁵ / 1.6×10⁻¹⁹ = 2×10⁴ N/C = 20 kV/m **Example 2 (Point Charge):** Find field 0.5 m from a +5 nC charge. • Source charge = 5×10⁻⁹ C • Distance = 0.5 m • k = 8.99×10⁹ N·m²/C² • E = (8.99×10⁹ × 5×10⁻⁹) / (0.5)² = 179.8 N/C **Example 3 (Strong Field):** Field 1 cm from a -10 μC charge. • Source charge = 10×10⁻⁶ C • Distance = 0.01 m • E = (8.99×10⁹ × 10×10⁻⁶) / (0.01)² • E = 8.99×10⁸ N/C = 899 MV/m (very strong!) **Example 4 (Uniform Field between Plates):** Parallel plates with 1000 V potential difference, 2 cm apart. • E = V/d = 1000 V / 0.02 m = 50,000 V/m = 50 kV/m **Example 5 (Superposition):** Two charges: +3 nC at origin, -2 nC at 4 m. Find field at 2 m. • E₁ = (8.99×10⁹ × 3×10⁻⁹) / 2² = 6.74 N/C (→) • E₂ = (8.99×10⁹ × 2×10⁻⁹) / 2² = 4.50 N/C (→) • E_total = 6.74 + 4.50 = 11.24 N/C (→) (Both point right since one repels and other attracts in same direction)

What is an electric field?

An electric field is a region around a charged particle where other charges experience a force. Field strength E is force per unit charge (N/C), indicating how strongly a +1 C test charge would be pushed or pulled.

What are the electric field formulas?

Two main formulas: E = F/q (field from force on a test charge), and E = kQ/r² (field from a point charge). Both give field strength in N/C or V/m. k = 8.99×10⁹ N·m²/C² is Coulomb's constant.

What is the difference between N/C and V/m?

They're equivalent units for electric field! N/C (newtons per coulomb) emphasizes force, while V/m (volts per meter) emphasizes potential. 1 N/C = 1 V/m. Use whichever is more intuitive for your problem.

How do electric field lines work?

Field lines show electric field direction. They point away from positive charges and toward negative charges. Line density indicates field strength - closer lines mean stronger field. Lines never cross.

What is Coulomb's Law?

Coulomb's Law describes force between charges: F = kq₁q₂/r². Combined with E = F/q, this gives the point charge field formula E = kQ/r². The electric field is Coulomb's Law per unit charge.

Can electric field be negative?

Electric field is a vector with direction. "Negative" E typically means the field points toward the source charge (negative charge) or in the negative coordinate direction. Magnitude is always positive.

What is electric field superposition?

The total electric field from multiple charges is the vector sum of individual fields: E_total = E₁ + E₂ + E₃ + ... This principle applies to any charge configuration.

How does distance affect electric field?

For a point charge, field strength decreases with the square of distance: E ∝ 1/r². Double the distance, field drops to 1/4. This is the inverse square law, similar to gravity and light intensity.

What is uniform electric field?

A uniform electric field has constant magnitude and direction, like between parallel plates: E = V/d, where V is voltage and d is separation. Field lines are parallel and evenly spaced.

How do conductors affect electric fields?

Inside a conductor, electric field is zero (charges redistribute to cancel it). Field just outside is perpendicular to the surface. Conductors shield their interiors from external fields (Faraday cage).

What are typical electric field strengths?

Air breaks down at ~3×10⁶ V/m. Atmosphere: ~100 V/m downward. Inside atoms: ~10¹¹ V/m. Between capacitor plates: 10³-10⁷ V/m. Lightning: ~10⁶ V/m. Household wiring: ~10-100 V/m nearby.

How is electric field related to electric potential?

Electric field is the negative gradient of potential: E = -dV/dx. For uniform fields, E = ΔV/Δx. Field points from high to low potential. Moving with the field decreases potential energy for positive charges.