Solved: A cube is located with one corner situated at the

Chapter 18, Problem 19.85

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A cube is located with one corner situated at the origin of an x, y, z coordinate system. One of the cubes faces lies in the x, y plane, another in the y, z plane, and another in the x, z plane. In other words, the cube is in the first octant of the coordinate system. The edges of the cube are 0.20 m long. A uniform electric field is parallel to the x, y plane and points in the direction of the y axis. The magnitude of the field is 1500 N/C. (a) Using the outward normal for each face of the cube, find the electric flux through each of the six faces. (b) Add the six values obtained in part (a) to show that the electric flux through the cubical surface is zero, as Gauss law predicts, since there is no net charge within the cube.