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

Question

A nonuniform 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 0.20 m in diameter, is aligned parallel to the x-axis, as shown in the figure. The electric fields E 1 and E 2, at the ends of the cylindrical surface, have magnitudes of 6000 N/C and 2000 N/C respectively, and are directed as shown. ( 0 = 8.85 × 10-12 C2/N · m2) The charge enclosed by the cylindrical surface is closest to

Explanation / Answer

gauss law for cylinder

phi = Qenc./e0

Phi(curved surface) - E1*pi*r^2 + E2*pi*r^2 = Qenc./e0

Qenc. = e0*pi*r^2(E2 - E1) = 8.85*10^-12*3.14*0.1*0.1*(2000 - 6000) = -1.11*10^-9 C

Qenc = -1.11 nC

Correct answer is option B.

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