A square copper plate 1.0 cm thick, 2.0 meters on a side, has a total excess cha

Question

A square copper plate 1.0 cm thick, 2.0 meters on a side, has a total excess charge of Q_total = 48 nC. You decide to use Gauss's law to find the electric field a distance of 2.0 mm from the center of the plate. Add '+' signs to the Side View sketch to show the location of the electric charge, and add vectors to show the electric field. Point P is 2.0 mm above the surface, and is located in the top of a Gaussian cylinder of radius r that has its lower end inside the copper plate. Give the flux through each of these parts of the cylindrical Gaussian surface, in terms of E, r, and any other variables needed: Circular top Curved sides Circular bottom

Explanation / Answer

a) Gauss law

total flux coming out of the surface = phi = integral E.dS = Qenclosed/Eo

=> E*A = Q/Eo , where A is area of square gaussian surface

=> E = 48*10^-9 /(4*8.85*10^-12) = 1.355*10^3 v/m

b) flux through circular top = Q/Eo = 48*10^-9/(8.85*10^-12) = 5.42*10^3 wb

flux thriugh curved sides = 0

flux through circular bottom = 0

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