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Gauss's law
Intermediate
Flux through a closed surface equals enclosed charge over ε₀.
∮E·dA = q/ε₀The net flux through any closed surface equals the enclosed charge divided by ε₀: ∮E·dA = Q_enc/ε₀. It makes fields of symmetrical charge distributions easy.
A sphere with 1 nC enclosed: Φ = 113 N·m²/C.
Only enclosed charges count, but all charges produce the field.
In more detail
Gauss's law states that the total electric flux through a closed surface equals the enclosed charge divided by the permittivity of free space. It is a powerful tool for symmetric charge distributions.
Real-world uses
- Gauss's law gives fields of spheres, cylinders and planes simply.
- Physicists use it to derive the field inside conductors.
- Physicists use Gauss's law to find the electric field of a symmetrical charge distribution, such as a long wire or a sphere.
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Frequently asked questions
Does charge outside the surface matter?
No, only the enclosed charge contributes to the total flux.
When is Gauss's law most useful?
When the charge distribution has symmetry that makes the field constant over a chosen surface.
When is Gauss's law easy to use?
When the charge has symmetry, such as spherical, cylindrical or planar, so the field is constant over the chosen surface.
Related topics in Electrostatics
Torque on a dipole in a field · Potential energy of a dipole · Electric flux · Field of infinite line charge · Field of infinite plane sheet · Field of a charged shell