Figure 16-28 shows a prism-shaped object that is 40.0 cm high, 30.0 cm deep, and 80.0 cm long.

step 1 This problem covers the concept of the electric flux and the electric flux is given by this equa

Figure 16-28 shows a prism-shaped object that is 40.0 cm...

Figure $16-28$ shows a prism-shaped object that is $40.0 \mathrm{~cm}$ high, $30.0$ $\mathrm{cm}$ deep, and $80.0 \mathrm{~cm}$ long. The prism is immersed in a uniform electric field of $500 \mathrm{~N} / \mathrm{C}$ directed parallel to the $x$ axis. (a) Calculate the electric flux out of each of its five faces and (b) the net electric flux out of the entire closed surface. (c) If in addition to the given electric field the prism also enclosed a point charge of $-2.00 \mu \mathrm{C}$, qualitatively how would your answers above change, if at all?

Key Concepts

Uniform Electric Field

A uniform electric field is one in which the electric field vector has the same magnitude and direction at every point in space. This simplification allows for straightforward calculations of electric flux through surfaces, as the field can be treated as constant over these surfaces.

Surface Orientation

The orientation of a surface, typically defined by its normal vector, is critical when calculating electric flux. The flux through a face depends on the cosine of the angle between the electric field and the area vector, which makes it essential to consider the relative alignment of the electric field with each surface of an object.

Electric Flux

Electric flux is a measure of the amount of electric field passing through a given surface. It is mathematically defined as the surface integral of the electric field over an area, taking into account the orientation of the surface. This concept is crucial for understanding how different parts of an object interact with an external electric field.

Gauss's Law

Gauss's law is a fundamental principle in electromagnetism that relates the net electric flux through a closed surface to the total electric charge enclosed by that surface. This law provides a powerful method to calculate electric fields and fluxes without directly performing difficult integrals, especially in systems with high symmetry.

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