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Physics II

Gauss Law

Syeilendra Pramuditya

Physics Study ProgramInstitut Teknologi Bandung

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Carl Friedrich Gauss

German Mathematician and Physicist (1777 - 1855)

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The Flux

Flux id the scalar (or dot) product of an area and the field across that area

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Flux of an Electric Field

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Gauss Law

Gauss law relates net flux through Gaussian surface and net enclosed charge

We know the net flux we know the net enclosed charge

We know the net enclosed charge we know the net flux

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Gauss Law

Surface S1: all-outward electric field positive flux positive net

enclosed chargeSurface S2: all-inward electric field

negative flux negative net enclosed chargeSurface S3: zero net enclosed charge zero net fluxSurface S4: zero net enclosed charge zero net flux

Four Gaussian surfaces

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Gauss and Coulomb Laws: Relation?Both describe the relation between electric charge and electric field

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Charged Isolated Conductor

A lump of metal with charge of +qWhere is the charge?Gaussian surface just inside the real surfaceNo electrical current inside no moving conduction electrons no electrical field“Electric field inside a conductor is ALWAYS zero”E = 0 Φ MUST be zeroΦ = 0 qenc MUST be zero“Charge in a conductor ALWAYS lies on its surface”

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Isolated Conductor with a Cavity

Where is the charge?Gaussian surface inside the cavityWe already know: E = 0 inside a conductorE = 0 Φ MUST be zeroΦ = 0 qenc MUST be zero“There is NEVER a net charge on cavity wall inside a conductor”

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External Electric FieldHow is the electric field outside?

Spherical conductor charge is uniformly distributed (uniform σ)All other geometries charge is NOT uniformly distributed (non-uniform σ)

Draw a cylindrical Gaussian surfaceInternal end cap E = 0 Internal curved surface E = 0 External curved surface E = 0 External end cap E is NOT zero