A cube is located with one corner situated at the origin of an x, y, z coordinat

Question

A cube is located with one corner situated at the origin of an x, y, z coordinate system. One of the cube's 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 0.22 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 1570 N/C. (a) Using the outward normal for each face of the cube, find the electric flux through each of the six faces. (Let the side of the cube in the x, z plane be the bottom of the cube, the side of the cube in the z, y plane be the left side of the cube, and the side of the cube in the x, y plane be the back of the cube.) (?E)bottom = __N

Explanation / Answer

(a) It would be confusing to say "top" or "bottom" face. Face(0, y, z): zero electric flux Face(0.2, y, z): zero electric flux Face(x, 0, z): electric flux = -60 N/C Face(x, 0.2, z): electric flux = +60 N/C Face(x, y, 0): zero electric flux Face(x, y, 0.2): zero electric flux (B) Add the six values obtained above, the result is clearly zero.

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