Electric Field Calculator
Calculates electric field strength, electrostatic force, or electric potential for point charges in any medium. Use it when solving Coulomb's-law problems or designing capacitor and sensor systems.
About this calculator
The electric field E produced by a point charge Q at distance r is given by E = kQ / (εᵣ · r²), where k = 8.99 × 10⁹ N·m²/C² is Coulomb's constant and εᵣ is the relative permittivity of the medium. The electrostatic force on a test charge q in that field is F = kQq / (εᵣ · r²), which is simply F = qE. The electric potential V at distance r is V = kQ / (εᵣ · r). All three quantities decrease as distance increases, but field and force fall off with the square of distance while potential falls off linearly. The medium matters: water (εᵣ ≈ 80) reduces field strength dramatically compared to vacuum (εᵣ = 1). This calculator normalises the permittivity input to ε₀ = 8.854 × 10⁻¹² F/m so you can enter absolute permittivity directly.
How to use
Suppose a source charge Q = 2 × 10⁻⁶ C sits in air (ε ≈ ε₀ = 8.854 × 10⁻¹² F/m) and you want the electric field 0.3 m away. Select 'Field' as the calculation type. Enter charge = 2 × 10⁻⁶ C, distance = 0.3 m, and medium = 8.854 × 10⁻¹² F/m. The calculator evaluates E = (8.99 × 10⁹ × 2 × 10⁻⁶) / (0.3² × 1) = 17,980 / 0.09 ≈ 199,778 N/C, or roughly 2.0 × 10⁵ N/C pointing away from the positive charge.
Frequently asked questions
What is the difference between electric field and electrostatic force?
Electric field E is a property of space created by a source charge; it exists whether or not a second charge is present and is measured in N/C or V/m. Electrostatic force F is the actual push or pull experienced by a specific test charge q placed in that field, given by F = qE. The field description is more useful in physics because it lets you predict the force on any charge without recalculating from scratch.
How does the medium affect electric field strength?
The medium's permittivity εᵣ appears in the denominator of Coulomb's law, so a higher permittivity reduces the field strength proportionally. In vacuum εᵣ = 1, in air it is ≈ 1.0006 (essentially 1), and in water it is ≈ 80, meaning the field is 80 times weaker than in vacuum at the same distance. This shielding effect is why ionic compounds dissolve easily in water — the electrostatic attraction between ions is greatly weakened.
Why does the electric field fall off with the square of the distance from a point charge?
A point charge radiates its influence uniformly in all directions. Imagine the field lines spreading over the surface of a sphere of radius r; that surface area grows as 4πr², so the field strength — proportional to lines per unit area — must decrease as 1/r². This inverse-square relationship is a geometric consequence of living in three-dimensional space and applies equally to gravity, light intensity, and sound pressure far from a point source.