A non-uniform electric field is directed along the x-axis at all points in space

Question

A non-uniform electric field is directed along the x-axis at all points in space. This magnitude of the field varies with x, but not with respect to y or z. The axis of a cylindrical surface, 0.80 m long and 0.23 m in diameter, is aligned parallel to the x-axis, as shown in the figure. The electric fields E1 and E2, at the ends of the cylindrical surface, have magnitudes of 5120 N/C and 963 N/C respectively, and are directed as shown. What is the net electric flux passing through the cylindrical surface? (Give your answer to the nearest N m2/C).

Explanation / Answer

surafce area of flat circular part,

A = pi r^2 = pi (0.23/2)^2 = 0.0415 m^2

flux = E.A

flux1 = 5120 x 0.0415 x cos180 = - 212.7 N m^2 / C

flux2 = 963 x 0.0415 x cos0 = 40.01 N m^2 /C

net flux = flux1 + flux2 = -172.7 N m^2 / C

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