The cube in the figure (Figure 1) has sides of length L=10.0cm. The electric fie

Question

The cube in the figure (Figure 1) has sides of length L=10.0cm. The electric field is uniform, has a magnitude E=4.00×103N/C, and is parallel to the xy-plane at an angle of 36.9 measured from the +xaxis toward the +yaxis. A)What is the electric flux through the cube face S1? B)What is the electric flux through the cube face S2? C)What is the electric flux through the cube face S3? D)What is the electric flux through the cube face S4? E)What is the electric flux through the cube face S5? F)What is the electric flux through the cube face S6? G)What is the total electric flux through all faces of the cube?

Explanation / Answer

E = 4 * 103 N/C

theta = 90 - 36.9 = 53.1 deg

L = 10 cm = 0.1 m

A = 0.12 = 0.01 m2

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Electric flux through S2 and S4 = 0

phiS2 = phiS4 = 0

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Ex = E * cos theta = 4 * 103 * cos 53.1 = 4 * 103 * 0.60 = 2400 N/C

Ey = E * sin theta = 4 * 103 * sin 53.1 = 4 * 103 * 0.799 = 3196 N/C

phiS3 = - phiS1 = 0.01 * 3196 = 31.96 Nm2/C

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phiS5 = - phiS6 = 0.01 * 2400 = 24 Nm2/C

phitotal = 0

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