Final answer:
Gauss's Law can be applied to two parallel plates by considering a cylindrical Gaussian surface to simplify the electric flux to the charge present on one plate divided by the permittivity of vacuum. This is possible due to the planar symmetry and uniform electric field between the plates.
Step-by-step explanation:
When applying Gauss's Law to the case of two plates, we are typically referring to two parallel conducting plates, which is a configuration that exhibits planar symmetry. The electric field between two such plates is uniform, and thus, the selection of a Gaussian surface becomes a matter of convenience.
To apply Gauss's Law, we would consider a cylindrical Gaussian surface with its sides parallel to the plates to determine the electric field. The electric field lines between the plates are perpendicular to the surface, and according to Gauss's Law, the electric flux through this closed cylindrical surface would be equal to the charge present on one plate divided by the permittivity of vacuum (ε0).
This simplification is possible because the electric field on the sides of the cylinder is parallel to the surface, meaning there is no flux through these sides, and the electric field at the base and top of the cylinder (within the plates) is uniform. Therefore, the integral simplifies to E ⋅ A where E is the magnitude of the electric field and A is the area of the plate.
By understanding the symmetry of the charge distribution and choosing an appropriate Gaussian surface, we can use Gauss's law to relate the electric flux through that surface to the net charge enclosed, which in the case of two parallel plates, can yield the electric field strength between them.