(II) A cube of side l is placed in a uniform field E=6.50 ×10^3 N / C with edges parallel to the

step 1 Hello. For problem 16 .46, we are asked to find the electric flux through a cube. For Part A, we

(II) A cube of side l is placed in a uniform field E=6.50...

(II) A cube of side $l$ is placed in a uniform field $E=6.50 \times 10^{3} \mathrm{N} / \mathrm{C}$ with edges parallel to the field lines. (a) What is the net flux through the cube? (b) What is the flux through each of its six faces?

Key Concepts

Symmetry in Flux Distribution

Symmetry considerations allow for simplified calculations of flux through different portions of a closed surface. In a uniform electric field interacting with a symmetric object such as a cube, it is possible to deduce the contributions to the total flux through various faces based on their orientations relative to the field. This understanding helps in partitioning the net flux among faces even when the net flux through the entire closed surface is zero.

Uniform Electric Field

A uniform electric field has the same magnitude and direction at every point in space. This constancy allows for simplified calculations of electric flux, especially over flat surfaces or symmetric objects, because the electric field does not vary over the surface area being considered. The field’s uniformity is a key assumption that simplifies the evaluation of flux distributions in problems involving regular geometric shapes.

Gauss’s Law

Gauss’s Law relates the net electric flux through a closed surface to the electric charge enclosed by that surface. It is expressed mathematically as ? = Q_enc/??, where ? is the total flux, Q_enc is the enclosed charge, and ?? is the permittivity of free space. In scenarios where there is no charge inside the closed surface, the net electric flux is zero, regardless of the external electric field configuration.

Electric Flux

Electric flux is a measure of the number of electric field lines passing through a given surface. It is calculated using the integral ? = ? E · dA, where E is the electric field and dA is the differential area element. The calculation takes into account the angle between the electric field and the normal to the surface, making it essential for understanding how the electric field interacts with complex surfaces.

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