Question

does the electric field near a large sheet of charge depend on the distance, why? Explain in detail.

Answer 1

No,  the electric field near a large sheet of charge does not depend on the distance.

The essential idea is this: When you come closer to the plane, the magnitude of of the field due to every infinitesimal piece of the plane is large. But since field is a vector, its direction is important too. When you are close to the surface, the field contributions from most of the parts of the plane are almost parallel to the surface, and all parallel contributions cancel off because of symmetry. As you move away from the surface, though the magnitudes of the individual field contributions are reduced, the field contributions start becoming more and more perpendicular to the plane and there is no symmetry-based cancellation for the perpendicular component. The force being inverse squared means that the two effects will nullify each other perfectly and the field remains constant.