AP Physics C E and M 8.5: Electric Flux

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

[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 8.5.A—Describe the electric flux through an arbitrary area or geometric shape 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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8.5.A—Describe the electric flux through an arbitrary area or geometric shape question 1