Gauss Law Calculator

What Is Gauss's Law?

Gauss's law relates the electric flux through a closed surface to the charge enclosed within it: Φ = Q / ε₀, where ε₀ = 8.854 × 10⁻¹² F/m is the permittivity of free space. For a point charge inside a spherical Gaussian surface of radius r, the electric field magnitude is E = Q / (4πε₀r²).

Spherical Symmetry

When charge distribution has spherical symmetry, the field is radial and uniform over any concentric sphere. The flux integral simplifies to E × 4πr² = Q / ε₀. This lets you solve for electric field, enclosed charge, flux, or radius depending on what is known.

Key Relationships

• Electric flux: Φ = Q / ε₀ (total flux through any enclosing surface)
• Electric field: E = Q / (4πε₀r²) (at distance r from point charge)
• Enclosed charge: Q = Φ × ε₀