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

ID: 1513856 • Letter: A

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 9000 N/C and 4000 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

-3.0 nC. -1.4 nC. 1.4 nC. 6.0 nC. -6.0 nC.

Explanation / Answer

here,
length of cyclinder, l = 0.80 m
radius of cyc, r = 0.2/2 = 0.1 m
Electric fiedl, E1 = 9000 N/C and E2 = 4000 N/C


from gauss law, charge enclosed by surface :
Q = (E2 - E1) * A*eo
Q = (4000 - 9000) * pi * 0.1^2 * 8.85 * 10^-12
Q = -1.4*10^-9 C or -1.4 nC

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