A slab of insulating material (not metal!) with infinite area (infinite y-z plan

Question

A slab of insulating material (not metal!) with infinite area (infinite y-z plane) has a uniform positive charge density rho . An edge view of the slab is shown in the figure on the right. You will find the electric field E inside the slab at distance x from the center (O). Imagine a rectangular solid as a Gaussian surface of area A and thickness t (in x direction) inside the slab. Assume the left surface of the Gaussian surface is at x = 0 (on the y-z plane). It is clear that electric field E, if any, is perpendicular to the y-axis and in the positive or negative x direction. Find the net flux that penetrates the Gaussian surface in terms of E at x = t (denote it by E(t)) and A. Note E(0) is not the same as E(t). Find the amount of charge inside the Gaussian surface in terms of A, t, and rho .

Explanation / Answer

(a)Electric field at the center of the slab is 0 because the charge is uniformly distributed throughout the slab. So E(0) = 0.

Electric field at the surface at x=t is E(t) . So, the total flux leaving the gaussian surface with area A is E(0)*A + E(t)*A = E(t)*A

(b) Amount of charge enclosed = volume * charge density = A*t*

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