Use Stokes theorem to find the circulation . V dr of the vector field V = yi + x*j – 5zyk around the boundary C of the right cylindrical surface of radius r = 1 and height h = 2, which base lies on the (x, y) plane, as shown in the figure. h=2 C

A flat sheet is in the shape of a rectangle with sides of lengths 0.400 m and 0.600 m. The sheet is immersed in a uniform electric field of magnitude 55.0 N/C that is directed at 20 degrees from the plane of the sheet (Figure 1). Find the magnitude of the electric flux through the sheet. Express your answer with the appropriate units.

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What is the net electric flux through the cylinder (a) shown in (Figure 1)?   What is the net electric flux through the cylinder (b) shown in (Figure 2)?   Express your answer in terms of the variables E, R, and the constant π.