1. Three infinite conducting planes are parallel to the y-z plane and placed at the points x=0, x-a, and x - 2a (a > 0)

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1 Three Infinite Conducting Planes Are Parallel To The Y Z Plane And Placed At The Points X 0 X A And X 2a A 0 1 (42.62 KiB) Viewed 49 times

1. Three infinite conducting planes are parallel to the y-z plane and placed at the points x=0, x-a, and x - 2a (a > 0) along the x-axis. With this arrangement, the conducting planes break space up into four regions, as noted in the table and figure below. Assume that the electric potential is constant on planes that are parallel to the y-z plane (in other words, Vis solely a function of x and not a function of y and 2). The potential Vis given as follows (see figure below): Region Electric potential V Range in x x < 0 I V = 0 II 0 < x <a V = -Vox² III a < x < 2a V = (x-2a)Va V = 0 IV x 2a The electric permittivity is equal to Eo in all four regions. (a) Determine the electric field E for each of the four regions. [5 points] (b) Find the volume charge density p for each of the four regions. [5 points] (c) Calculate the surface charge density o for each of the three conducting planes. (Hint: Recall the boundary conditions for the electric field and/or potential when crossing a conducting, charged plane. If you don't remember them, try using a Gaussian pillbox approach to derive them.) [10 points]