Gauss's Law & Electric Flux Lab

Apply Gauss's Law to calculate electric fields and flux for symmetric charge distributions. Choose point charges, line charges, infinite planes, spheres, or cylinders, set the Gaussian surface, and see results instantly.

Guided Experiment: Gauss's Law for a Sphere

How does the E-field vary with distance r for a uniformly charged sphere? What happens inside the sphere versus outside?

Write your hypothesis in the Lab Report panel, then click Next.

Controls

rChargeGaussian Surface

Results

Distribution
Point Charge
Enclosed Charge
Electric Flux (Gauss's Law)
E-field at Gaussian Surface
Gaussian Surface
Radius r = 0.1 m

Data Table

(0 rows)
#DistributionCharge / λ / σr (m)Q_enc (C)Φ (N·m²/C)E (N/C)
0 / 500
0 / 500
0 / 500

Reference Guide

Gauss's Law Statement

The net electric flux through any closed surface equals the enclosed charge divided by the permittivity of free space.

EdA=Qencε0\oint \vec{E} \cdot d\vec{A} = \frac{Q_{\text{enc}}}{\varepsilon_0}

This holds for any closed surface, regardless of shape, but is most useful when symmetry lets us pull E out of the integral.

Symmetry & Gaussian Surfaces

The key to applying Gauss's Law is choosing the right Gaussian surface that matches the symmetry of the charge distribution.

  • Spherical for point charges and spheres
  • Cylindrical for line charges and cylinders
  • Pillbox for infinite planes

On a well-chosen surface, E is constant and parallel to dA, so the integral simplifies to E times the area.

E-Field from Gauss's Law

Once symmetry simplifies the integral, solving for E gives familiar results.

Point: E=Q4πε0r2\text{Point: } E = \frac{Q}{4\pi\varepsilon_0 r^2}
Line: E=λ2πε0r\text{Line: } E = \frac{\lambda}{2\pi\varepsilon_0 r}
Plane: E=σ2ε0\text{Plane: } E = \frac{\sigma}{2\varepsilon_0}

Applications

Gauss's Law is one of Maxwell's four equations and is fundamental to understanding electrostatics.

  • Finding E-fields for conductors and insulators
  • Proving E = 0 inside a conducting shell
  • Designing capacitors (parallel plate, cylindrical, spherical)
  • Understanding charge shielding (Faraday cage)

Inside a uniformly charged sphere, E grows linearly with r. Outside, it behaves exactly like a point charge.