Question

What is the difference between a sheet of charge and a plane conductor having a charge?

Answer 1

We will answer this question by directly stating the differences between a sheet of charge and a plane conductor having a charge. First we will mention differences based on their dimensions and at last then their properties (conducting or non-conducting).

Complete step by step solution:
Let us have a look on few differences:

Sheet of charge	Plane conductor
1. The term "plane sheet of charge" refers to a two-dimensional flat surface with an endless number of charges. The sheet does not have to be a conductor; it can be an insulator that holds charges.	1. The charge on a conducting surface can interact with other changes on the other side of the boundary. Similar to a spherical solid conducting sheet in which charges are distributed uniformly throughout the volume, but all of the charges are concentrated on the surface to achieve extreme potential and form an equipotential surface. Charges can't come to the surface if it's a non-conducting surface.
2. The electric flow in a plane charged sheet (infinite) is on both surfaces (which may be easily determined by considering a cylindrical Gaussian surface). $E = \dfrac{\sigma }{{2\varepsilon }} + \dfrac{\sigma }{{2\varepsilon }} = \dfrac{\sigma }{\varepsilon }$ is the outcome.	2. When considering the electric flux of a conducting surface, there is just one surface to consider. It can also be found, like in the previous situation. $E = \dfrac{\sigma }{\varepsilon }$ is the outcome.

Note:
Simply grasp the use of Gauss law through these examples and apply it wherever it is required. Keep in mind that the "surface charge density" term you employ should be compatible with the theories you utilise to solve a problem.