⚡ Electric Field Calculator – Point Charge Strength & Direction
The Electric Field Calculator helps students, engineers, and physicists instantly compute the electric field strength produced by a point charge at any observation distance. Using Coulomb's fundamental law, it also calculates electric potential, optional force on a test charge, and supports multi-charge superposition analysis — all with full unit conversion support.
What Is an Electric Field?
An electric field is an invisible force field that surrounds every electric charge. When a charged particle (source charge) is placed in space, it creates a field that exerts a force on any other charged particle placed within it. The electric field strength, denoted E, represents the force experienced by a unit positive test charge at a given point.
Electric fields are fundamental to understanding how electronics work, how lightning forms, how capacitors store energy, and how electromagnetic waves propagate through space.
The Electric Field Formula
For a single point charge, the electric field at distance r is given by:
E = k × |q| / r²Where:
- E = electric field strength (N/C or V/m)
- k = Coulomb's constant = 8.9875517923 × 10⁹ N·m²/C²
- q = source charge magnitude (Coulombs)
- r = distance from the charge (meters)
The field follows an inverse-square law: doubling the distance reduces the field strength by a factor of four. This is identical in form to gravitational fields, making electric fields a foundational concept in classical physics.
Electric Field Direction
The direction of an electric field is defined as the direction a positive test charge would move when placed in the field:
- Positive source charge: field lines point away (radially outward). A positive test charge is repelled.
- Negative source charge: field lines point toward the charge (radially inward). A positive test charge is attracted.
Electric Potential
Alongside the electric field, this calculator computes the electric potential at the observation point:
V = k × q / rUnlike the electric field, potential is a scalar quantity (no direction) and can be positive or negative depending on the charge sign. The SI unit is Volts (V). Electric field and potential are related by:
E = −dV/drForce on a Test Charge
Once the electric field is known, the force on any test charge placed at that point is:
F = q_test × EThis is Newton's law applied to electrostatics. Enable the Test Charge option in the calculator to see the exact force — useful for solving circuit problems, ion motion analysis, and electromagnetic simulations.
Superposition Principle
When multiple charges are present, the total electric field at any point is the vector sum of the fields from each individual charge:
E_total = E₁ + E₂ + E₃ + ...The Superposition tab lets you add multiple charges, specify each charge's distance and angular position, and compute the net field automatically. This is essential for analyzing charge distributions in capacitors, dipoles, and multi-electrode systems.
Supported Units
| Quantity | Supported Units |
|---|---|
| Charge | C, mC, µC, nC, pC |
| Distance | m, cm, mm, km, ft, in |
| Electric Field | N/C = V/m, kN/C |
| Electric Potential | V, kV |
| Medium | Vacuum, Air, Custom εᵣ |
Effect of Medium (Permittivity)
In materials other than vacuum, the effective Coulomb's constant is reduced by the medium's relative permittivity (εᵣ, also called dielectric constant):
k_eff = k₀ / εᵣFor vacuum, εᵣ = 1. For air, εᵣ ≈ 1.0006 (practically the same as vacuum). For water, εᵣ ≈ 80, meaning the electric field is 80 times weaker at the same distance. This explains why ionic compounds dissolve easily in water.
Common Applications
- Capacitor design: calculating field strength between parallel plates
- Particle physics: analyzing forces on ions and electrons
- Electrostatic shielding: understanding Faraday cage principles
- Lightning rods: point discharge and field concentration
- Medical devices: electric fields in ECG sensors and defibrillators
- Student coursework: solving physics problems involving Coulomb's law
Quick Reference: Electric Field vs. Distance
| Charge (µC) | Distance | Electric Field |
|---|---|---|
| 1 µC | 0.1 m | 899,755 N/C |
| 1 µC | 0.5 m | 35,990 N/C |
| 1 µC | 1.0 m | 8,988 N/C |
| 5 µC | 0.2 m | 1,124,693 N/C |
| 10 µC | 1.0 m | 89,876 N/C |
Tips for Accurate Results
- Always ensure the distance value is greater than zero — the formula diverges as r → 0.
- Use µC (microcoulombs) for everyday lab-scale charges; use nC or pC for very small charges like those on charged dust particles.
- For multi-charge problems, set the angle carefully: 0° points right, 90° points up, 180° points left, 270° points down.
- Remember that 1 N/C = 1 V/m — they are the same unit expressed differently.