Question

Apply Gauss's law to determine the electric intensity at a point due to the infinite sheet of charge?????

Answer 1

Not sure what you mean by electric intensity.
Gauss's law gives the electric field easily enough: Consider a Gaussian pillbox shapeeach oval shape is of area dA, and the arrows are in the direction of E and dA, which coincide.\[\frac q\epsilon_0=\oint\overrightarrow{E}\cdot\overrightarrow{dA}=2EA\]Noting that we can write charge as charge density (sigma) times area\[\frac{\sigma A}{\epsilon_0}=2EA\to E=\frac{\sigma}{2\epsilon_0}\]Which you should notice is uniform throughout space.