A blue cube with an edge length of 85.90 cm has one of its edges coincident with

Question

A blue cube with an edge length of 85.90 cm has one of its edges coincident with the x-axis; the other two edges are parallel to the y and z axes, respectively. The cube exists in a region of space where the electric field is parallel to the x-axis and varies with x according to the following equation:

E = a + b x + c x2, where a = 6.21 N/C; b = 1.54 N/( C*m ); and c = 6.97 N/( C*m2).

The corner of the cube closest to the origin is located at x = 0.74

m. How much charge is contained inside the cube?

Explanation / Answer

Gauss' Law:

E.dA = Q/0

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E.dA = E(0.74)*L2 - E(0.74+L)*L2

E(0.74) = 6.21+1.54*0.74+6.97*0.742 = 11.166 N/m

E(0.74+L) = 6.21+1.54*(0.74+0.8590)+6.97*(0.74+0.8590)2 = 26.493 N/m

L2 = 0.8590*0.8590 = 0.737881 m2

E.dA = (-11.166+26.493)*0.737881 = 11.310

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Q = (E.dA)*0 = (11.310)*(8.85e-12) = 1.00 * 10^-10 C

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