An infinite plane of charge creates a uniform electric field that is perpendicular to the plane on both sides, and its strength does not depend on distance from the plane. Using Gauss’s law with a pillbox straddling the plane, the enclosed charge is σA and the total outward flux is E A on each side, so 2E A = σA/ε0, giving E = σ/(2ε0). The field points away from the plane for positive σ (toward it for negative σ). So the description that fits is a field perpendicular to the sheet with magnitude σ/(2ε0) on each side. The field is not parallel to the sheet, the magnitude isn’t ε0/σ, and the field is not zero.

Electric charge comes in two signs: positive and negative. Protons carry positive charge and electrons carry negative charge, so objects are charged when they have an excess or deficit of electrons; when there’s no net excess or deficit, the object is neutral. The two signs are fundamental because charges of opposite signs attract and like signs repel, and the magnitude of a charge is a multiple of the elementary charge. The other options describe states or material properties rather than the signs of charge: neutral vs charged is about having zero net charge, static vs dynamic refers to whether the charge is at rest or moving, and conducting vs insulating describes how easily charge flows in a material.

In a parallel-plate capacitor, the ability to store charge per volt scales with the overlapping plate area. With fixed separation d and dielectric ε, the capacitance is C = εε0 A / d. This means doubling the plate area doubles the capacitance, because each unit area behaves like its own tiny capacitor and these add in parallel. So increasing A increases C linearly, and the constant of proportionality εε0/d sets how large C becomes for a given area. The other options would require nonlinear, inverse, or no dependence on area, which contradicts the formula and the parallel arrangement.

The key idea is that inserting a dielectric between the plates increases the capacitor’s ability to store charge for the same voltage by a factor equal to the dielectric constant, κ. For a parallel-plate capacitor with vacuum, the capacitance is C0 = ε0 A / d. When a dielectric with relative permittivity κ fills the space, the permittivity becomes ε = ε0 κ, so the capacitance becomes C = ε A / d = ε0 κ A / d = κ C0. This means the new capacitance is larger by κ, not smaller or the same, and not κ squared. The dielectric reduces the electric field for the same charge, and that reduction directly translates into a larger capacitance by the factor κ.