AP Physics C: Electricity & Magnetism 8.5 A Describe the Electric Flux Through an Arbitrary Area or Geometric Shape Questions

Describe electric flux through an arbitrary area or geometric shape using the electric field, area vector, and surface orientation.

Exam points

identify zero, positive, or negative face flux from the electric field and outward area vector
derive total electric flux through a closed surface from its field or enclosed charge

[Maximum number: 2]

A very large nonconducting slab with a uniform positive volume charge density $\rho_{0}$ is fixed with the origin of the x y z-axes at its center, as shown in the figure above. The thickness of the slab is d, the length is L, and the width is W, where $L \gg d$ and $W \gg d$ . The large faces of the slab are parallel to the x y-plane.
Consider a Gaussian cylinder with a cross-sectional area A and height h that is positioned with its axis along the z-axis, as shown in the figure below.

Figure for Question AP Physics C: Electricity & Magnetism 8.5 A Describe the Electric Flux Through an Arbitrary Area or Geometric Shape Questions question 1 — AP Physics C: Electricity & Magnetism

Note: Figures not drawn to scale.

Use Gauss's law to derive expressions for the following. Express your answers in terms of $\rho_{0}, A, d, h, z$ , and physical constants, as appropriate.

Derive an expression for the total flux $\Phi$ through the Gaussian surface shown.

2 points
For using Gauss's law to calculate the electric flux 1 point
$\Phi=\frac{Q}{\varepsilon_{0}}=\frac{\rho V}{\varepsilon_{0}}$
For a correct answer 1 point
$\Phi=\frac{\rho_{0} A h}{\varepsilon_{0}}$

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AP Physics C: Electricity & Magnetism 8.5 A Describe the Electric Flux Through an Arbitrary Area or Geometric Shape Questions question 1