Gauss s law and symmetry
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Gauss’s Law and Symmetry. Kenny Smart Ethan Hatke. Electric Flux. Flux is the amount of an electric field that goes through an area Flux of the electric field is a scalar quantity. Gauss’s Law.

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Gauss’s Law and Symmetry

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Gauss s law and symmetry

Gauss’s Law and Symmetry

Kenny Smart

Ethan Hatke


Electric flux

Electric Flux

  • Flux is the amount of an electric field that goes through an area

  • Flux of the electric field is a scalar quantity


Gauss s law

Gauss’s Law

  • Gauss’s Law relates the total electric flux through a closed surface, the total charge enclosed by the surface, and the electric permittivity of free space

  • Gauss’s Law is commonly used to find the strength of an electric field produced by a single charge or a continuous distribution of charges

  • The area enclosing a charge we call a Gaussian shape, and is not a real object, just a tool to help solve electrostatic problems

  • Electric flux is negative when it is into the Gaussian surface, and positive when it is out of the Gaussian surface


Gauss s law and symmetry

λ,σ,ρ

  • λ is the linear charge density, usually of a wire, and describes the amount of charge per unit length

    • λ*L

  • σ is the area charge density, usually of a sheet or plate of charge, and describes the amount of charge per unit area

    • σ *A

  • ρ is the volumetric charge density, usually of nonconductors, and describes the amount of charge per unit volume

    • ρ*V


Conducting v nonconducting

Conducting v. Nonconducting

  • Conductors can’t hold an electric field inside their surface, all the like-charges repel each other and move to the outer radius of the object

  • Nonconductors can hold an electric field inside their surface because the charge is not free to move throughout the object and there are charges within the object, usually is a uniform field throughout the object but doesn’t have to be


Spherical symmetry

Spherical Symmetry

  • Within the inner sphere: No charge is enclosed so,

    =0 and there is no electric field within

  • In the donut at any point up to the outer radius, there is no net charge enclosed, and so there is no electric field and =0

  • At the outer radius of the donut: the charge enclosed is +Q and radius of R:, so (this is equivalent to Coulomb’s Law)

  • Beyond the outer radius, the electric field will decrease at a rate of 1/r^2 because the Gaussian shape is a sphere

Conducting sphere with charge +Q, inner radius r and outer radius of R


Cylindrical symmetry with a line of charge

Cylindrical Symmetry with a line of charge

Wire has linear charge density, λ, length L and radius r

  • A wire of charge is enclosed by a Gaussian cylinder

  • Qenclosed=λ*L

  • Area=2πrL


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