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# Gauss’s Law and Symmetry - PowerPoint PPT Presentation

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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Presentation Transcript

### Gauss’s Law and Symmetry

Kenny Smart

Ethan Hatke

• 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 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

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

• 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

• 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

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