Simulation · Physics · Class 12
Flux through a closed surface
From the lesson Gauss's law in Electric Charges and Fields. Change the values and watch what happens.
Flux through a closed surfacePhysics · Class 12
The idea behind it
NCERT §1.13
- For a point charge q at the centre of a sphere of radius r, E is the same everywhere on the sphere and along the normal, so the flux is E × 4πr² = q/ε₀, whatever the radius.
- Gauss's law: the total electric flux through any closed surface equals 1/ε₀ times the net charge enclosed, φ = ∮E·dS = q_enc/ε₀.
- It holds for a closed surface of any shape or size; the enclosed charges may lie anywhere inside it.
- q_enc counts only charges inside the surface, but the field E on the surface is produced by all charges, inside and outside.
- If a closed surface encloses no net charge, the total flux through it is zero, as for a closed cylinder in a uniform field: the flux in through one end equals the flux out through the other, and none crosses the curved side.
- The chosen surface is the Gaussian surface. It must not pass through a point charge (the field is undefined there), though it may pass through a continuous distribution.
- Gauss's law rests on the inverse-square form of Coulomb's law; it is most useful for finding E when the charge has symmetry.