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Gauss’s Law and Symmetry

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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 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

- 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