Gauss's Law and Its Applications
The net electric flux through a closed surface equals the enclosed charge divided by e0.
What is Gauss's Law and Its Applications?
The net electric flux through a closed surface equals the enclosed charge divided by e0.
Key formula / rule: Flux = qenclosed/e0, independent of the shape of the surface.
Key points
- Derive field expressions for symmetric charge distributions.
- Evaluate when Gauss's law is a practical tool.
Common exam trap
Assuming zero flux implies zero field on the surface.
Definitions
- Term
Gauss's Law and Its Applications
- Meaning
The net electric flux through a closed surface equals the enclosed charge divided by e0.
- Term
Gauss's Law and Its Applications — explanation
- Meaning
Gauss's law converts a hard integral into a one-line result whenever symmetry lets E be constant over a chosen surface. It gives the standard results for a line, a sheet and a shell.
Learning objectives
Derive field expressions for symmetric charge distributions.
Evaluate when Gauss's law is a practical tool.
Formulae
- Key point
Flux = qenclosed/e0, independent of the shape of the surface.
- Key point
Line charge: E = λ/(2 π e0 r); infinite sheet: E = σ/(2 e0).
- Key point
Field inside a uniformly charged conducting shell is zero.
Prerequisites
PHY-U5-ELS-T1-S1-C2
Common mistakes
Assuming zero flux implies zero field on the surface.
Applying Gauss's law where no symmetry exists and E cannot be taken out of the integral.
Keywords
Gauss
Applications
Practice preview
A uniform electric field E = 20 N/C exists in the positive x-direction. A square surface of side 10 cm is placed in the y-z plane. What is the electric flux through this surface?…
easy
An infinitely long straight wire has a uniform linear charge density λ. Using Gauss's Law, the magnitude of the electric field at a distance r from the wire is:…
medium
A point charge q is placed at one corner of a cube of side 'a'. What is the electric flux passing through one of the faces of the cube that does not contain the charge?…
hard