Electric Flux and Permittivity Calculator

Electric flux is a measure of the number of electric field lines passing through a given surface. It is defined as the surface integral of the electric field vector over a surface: Phi equals the integral of E dot dA. For a uniform electric field E perpendicular to a flat surface of area A, electric flux simply equals E times A. The SI unit for electric flux is V·m (volt-metres) or equivalently N·m²/C (newton-metres squared per coulomb). These two units are identical because 1 V = 1 N·m/C, so 1 V·m = 1 N·m²/C.

Gauss's law states that the total electric flux through any closed surface equals the net enclosed electric charge divided by the permittivity of free space (epsilon-zero). Written as an equation: Phi = Q_enclosed / epsilon_0. Rearranged: Q_enclosed = Phi times epsilon_0. Where epsilon_0 = 8.854187817 x 10^-12 F/m (farads per metre), the electric constant defined by NIST. Gauss's law is one of Maxwell's four equations of electromagnetism and is used to find electric fields in highly symmetric configurations such as spheres, cylinders, and infinite planes.

The units V·m (volt-metres) and N·m²/C (newton-metres squared per coulomb) are exactly equivalent. The relationship comes from the definition of the volt: 1 V = 1 J/C = 1 N·m/C. Therefore 1 V·m = 1 (N·m/C)·m = 1 N·m²/C. Physicists often write electric flux in N·m²/C when working from the definition of Gauss's law (which involves force and charge), and in V·m when working from electric potential. Both expressions appear in textbooks and literature.

Permittivity is a measure of how much resistance an electric field encounters when forming in a medium. The permittivity of free space (vacuum), epsilon_0, is a fundamental physical constant: 8.854187817 x 10^-12 F/m (farads per metre), also written as C²/(N·m²). Its value is defined in the 2019 SI revision from the defined value of the speed of light and the exact magnetic constant. The permittivity of any material is expressed as the product of epsilon_0 and the material's relative permittivity (dielectric constant): epsilon = epsilon_r times epsilon_0.

Relative permittivity (epsilon_r), also called the dielectric constant, is the ratio of a material's permittivity to that of vacuum. It is dimensionless. Vacuum has a relative permittivity of exactly 1.000. Air at standard conditions is 1.0006, meaning it behaves almost identically to vacuum. Polyethylene is about 2.25, glass ranges from 4 to 7, silicon is 11.7, and water at 20 degrees Celsius is about 80.1. Higher relative permittivity means the material can store more electric energy per unit volume in a capacitor. Values are published by NIST and IEEE standards.