Final answer:
The correct answer is b) The field of a sheet of charge is constant in magnitude and direction, and it is not a function of distance. This is confirmed by applying Gauss's law to a cylindrical Gaussian surface surrounding the sheet of charge.
Step-by-step explanation:
In determining the characteristics of the electric field due to an infinite sheet of charge using a cylindrical Gaussian surface, we find that the electric field is indeed perpendicular to the surface of the charge. Given the symmetry of the electric field and its independence from the distance to the charge sheet, we conclude that the correct answer is: b) The field of a sheet of charge is constant in magnitude and direction. It is not a function of distance.
The electric field does not vary with the height of the cylindrical Gaussian surface because the electric flux only crosses the ends of the cylinder, not the sides. Thus, applying Gauss's law, the electric field E corresponding to the charge density σ on the sheet is given by E = σ/ε0, where ε0 is the permittivity of free space. This expression confirms that the electric field is constant, not dependent on the distance from the sheet, and directed perpendicular to the surface of the charge.