10
N·m²/C
10
N·m²/C
1
0.02
m²
8.854187817e-11
C
500
N/C
0.02
m²
1
10
N·m²/C
10
N·m²/C
1
0.02
m²
8.854187817e-11
C
500
N/C
0.02
m²
1
The Electric Flux Calculator computes the electric flux through a flat surface placed in a uniform electric field. Electric flux is a measure of the number of electric field lines passing through a given area and is a central concept in electrostatics, forming the foundation of Gauss's Law—one of Maxwell's four equations of electromagnetism.
For a uniform electric field \(\vec{E}\) passing through a flat surface of area \(A\), the electric flux is defined as the dot product of the field and the area vector:
$$\Phi_E = \vec{E} \cdot \vec{A} = EA\cos\theta$$
where \(\theta\) is the angle between the electric field vector and the outward normal to the surface. When the field is perpendicular to the surface (\(\theta = 0°\)), the flux is maximum at \(EA\). When the field is parallel to the surface (\(\theta = 90°\)), no field lines pass through and the flux is zero.
The SI unit of electric flux is newton-meters squared per coulomb (N·m²/C), which is equivalent to volt-meters (V·m). Physically, flux quantifies how much of the electric field "flows" through a surface. A high flux means many field lines penetrate the surface; zero flux means the field is tangential or absent.
Electric flux is indispensable in electromagnetic theory. Gauss's Law states that the total electric flux through any closed surface equals the enclosed charge divided by the permittivity of free space: \(\Phi_E = Q_{\text{enc}} / \varepsilon_0\). This powerful relationship allows physicists and engineers to calculate electric fields for symmetric charge distributions (spheres, planes, cylinders) without performing complex integrals.
In practical applications, electric flux concepts appear in capacitor design (where the field between plates creates flux through the dielectric), electromagnetic shielding (Faraday cages work by redirecting flux), and antenna theory (radiation patterns are characterized by flux through surfaces). Environmental scientists even use analogous flux concepts to measure pollutant transport through atmospheric boundaries.
This calculator handles the general case of a uniform field at an arbitrary angle to a flat surface. It outputs the actual flux, the maximum possible flux, the cosine factor, and the equivalent enclosed charge (via Gauss's Law) that would produce that flux through a closed surface.
The electric flux through a flat surface in a uniform field is:
$$\Phi_E = E \cdot A \cdot \cos\theta$$
where \(E\) is the electric field magnitude (N/C), \(A\) is the surface area (m²), and \(\theta\) is the angle between the field direction and the surface normal.
Special cases:
$$\theta = 0° \Rightarrow \Phi = EA \quad \text{(maximum flux)}$$
$$\theta = 90° \Rightarrow \Phi = 0 \quad \text{(field parallel to surface)}$$
Equivalent enclosed charge (from Gauss's Law):
$$Q_{\text{enc}} = \Phi_E \cdot \varepsilon_0$$
where \(\varepsilon_0 = 8.854 \times 10^{-12}\) F/m is the permittivity of free space. This tells you what charge, if enclosed by a closed surface, would produce the calculated flux.
The electric flux value indicates how much of the electric field penetrates the surface. A flux of 10 N·m²/C means the surface captures 10 units of field-area product. The cos(θ) factor shows the geometric efficiency—at 0° it is 1.0 (fully efficient), at 60° it is 0.5, and at 90° it is 0. The equivalent enclosed charge gives physical meaning via Gauss's Law: it is the point charge that would create that same total flux through a surrounding closed surface.
Inputs
Results
A 500 N/C field passes perpendicularly through a 0.02 m² surface. The flux is 10 N·m²/C—the maximum possible for this field and area combination.
Inputs
Results
At 60°, only half the maximum flux passes through the surface. The 1000 N/C field through 0.05 m² gives 25 instead of 50 N·m²/C.
Electric flux represents the total number of electric field lines passing through a surface. More precisely, it is the surface integral of the electric field over an area. High flux means many field lines penetrate the surface; zero flux means the field runs parallel to the surface or there is no field present.
The angle \(\theta\) between the field and the surface normal determines how many field lines actually pass through the surface versus how many run alongside it. At \(\theta = 0°\), the field is fully perpendicular and all lines pass through. As \(\theta\) increases toward 90°, fewer lines cross the surface. The \(\cos\theta\) factor mathematically captures this geometric projection.
Yes. For a closed surface, inward flux is negative and outward flux is positive by convention. For an open surface, the sign depends on which direction you define as the outward normal. In this calculator, the angle range is 0°–90°, so flux is always non-negative. Angles beyond 90° would indicate field lines entering from the opposite side.
The SI unit of electric flux is N·m²/C (newton-meters squared per coulomb), which is equivalent to V·m (volt-meters). This unit arises naturally from multiplying the electric field (N/C) by area (m²).
Gauss's Law states that the total electric flux through any closed surface equals the enclosed charge divided by \(\varepsilon_0\): \(\oint \vec{E} \cdot d\vec{A} = Q_{\text{enc}} / \varepsilon_0\). This makes flux a bridge between field geometry and charge content. The "equivalent enclosed charge" in this calculator applies this relationship in reverse.
This calculator assumes a uniform (constant) electric field across the entire surface. For non-uniform fields, the flux must be computed as a surface integral: \(\Phi = \int \vec{E} \cdot d\vec{A}\). However, if the field variation is small across the surface, this calculator provides a good approximation using the average field strength.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
How helpful was this calculator?
Be the first to rate!
Coulomb's Law Calculator
Electrostatics Calculators
Electric Field Calculator
Electrostatics Calculators
Electric Potential Calculator
Electrostatics Calculators
Electric Potential Energy Calculator
Electrostatics Calculators
Capacitance Calculator
Electrostatics Calculators
Capacitor Energy Calculator
Electrostatics Calculators
