A 6.20-μC point charge is at the center of a cube with sides...

A $6.20-\mu \mathrm{C}$ point charge is at the center of a cube with sides of length 0.500 $\mathrm{m} .$ (a) What is the electric flux through one of the six faces of the cube? (b) How would your answer to part (a) change if the sides were 0.250 $\mathrm{m}$ long? Explain.

Key Concepts

Electric Flux

Electric flux is a measure of the number of electric field lines passing through a given surface. It is mathematically defined as the surface integral of the electric field over that surface, and it quantifies the field's spread in space relative to the geometry through which it passes.

Symmetry in Electrostatics

Utilizing symmetry in electrostatics, such as having a point charge at the center of a symmetrical shape like a cube, simplifies the analysis by ensuring that the electric field distributes uniformly over corresponding parts of the surface. This uniform distribution allows for equally dividing the total flux among equivalent faces or segments of the surface.

Gauss's Law

Gauss's law states that the total electric flux passing through a closed surface is equal to the enclosed charge divided by the permittivity of free space. This principle allows us to relate the net flux to the source charge without having to compute the detailed electric field distribution, especially in cases with high symmetry.

Insensitivity of Flux to Surface Size for a Central Charge

For a point charge located at the center of a symmetric closed surface, the total electric flux calculated by Gauss's law depends solely on the enclosed charge and not on the dimensions of the surface. Consequently, the flux through a specific segment, like one face of a cube, remains the same regardless of the cube's size as long as the symmetry is preserved.

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