A nonconducting sheet with a large surface area and a thickness d contains a uniform charge distribution of density ho . Determine the electric field at a point P located inside the plate, at a distance x from the central plane, and identify the qualitative shape of the graph of E against x for 0 < x < d .

Step-by-step solution

Consider a Gaussian pillbox symmetric about the central plane of the sheet, with cross-sectional area A and extending to a distance x on both sides. For a point inside the sheet ( 0 The charge enclosed by the Gaussian surface is q_ enclosed = (2xA) . Using Gauss's law, E d A = q_ enclosed ₀ E(2A) = (2xA) ₀ E = x ₀ Thus, the electric field increases linearly with x for 0 For a point outside the sheet ( x d 2 ): The total charge enclosed by the Gaussian surface is q_ enclosed = (dA) . Using Gauss's law, E(2A) = (dA)