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 E1 and E2, at the ends of the cylindrical surface, have magnitudes of 1000 N/C and 6000 N/C respectively, and are directed as shown. The net electric flux out of the cylindrical surface is closest to

Explanation / Answer

Refer above figure,

fTotal = a E1*dA + b E2*dA + c E3*dA................................f= flux

fTotal = E1dAcos180 + E2dAcos0 + E3dAcos90

fTotal = -E1A + E2A + 0

fTotal =A(-E1 + E2)

fTotal =r2(-E1 + E2)

fTotal =3.14*0.12(-1000 +6000)

fTotal = 157 N.m2/C

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