A cube is situated in three - dimensional space as shown. with its edges oriente

Question

A cube is situated in three - dimensional space as shown. with its edges oriented parallel to the coordinate axes. The length of each edge is 67.4 cm, and the area vector of each face points outward from the cube The region of the cube is occupied by a uniform field having strength 487 N/C and pointing in the direction of the positive x axis, (a) What is the flux through the "upstream" face of the cube, labeled "1" in the diagram? (b) What is the flux through the "downstream" face of the cube, labeled "2" in the diagram? (c) What is the flux through any of the other four faces of the cube? (d) What is the total flux through all the faces of the cube?

Explanation / Answer

(a) Flux = E A cos0 = E * l^2 = 487 * 0.674^2 = 221.232 (N/C) - m^2 (b) Flux = E A cos 180 = E * l^2 = -487 * 0.674^2 = -221.232 (N/C) - m^2 (c) Flux = E A cos 90 = 0 (N/C) - m^2 (d) Total flux = Flux in + Flux out = 221.232 - 221.232 = 0

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