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

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 0.31 m long. A uniform electric field is parallel to the x, yplane and points in the direction of the +y axis. The magnitude of the field is 1625 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.)

Explanation / Answer

Note that only the top and bottom faces have flux, since all the other sides are parallel to the field (faces have to be perpendicular to the field to have flux.)

Note that

Eflux = E A cos (theta)

where A = area of the face = s^2 = 0.0961 m^2
E = 1625 N/C
theta = the angle between the normal and the electric field

For the bottom face, theta = 180 degrees. Hence,

Bottom flux = -156.2 N m^2 /C [ANSWER]

For the top face, theta = 0 degrees. Thus,

Top flux = 156.2 N m^2/C [ANSWER]

For the front, back, left, and right faces, all theta = 90 degrees. Thus, for the other 4 faces,

[front, back, left, right] flux = 0 N m^2 /C [ANSWERS]

**************************************

b.

Adding all the results in the 6 faces, we see that they indeed sum to 0.

-156.2 + 156.2 + 0 + 0 + 0 + 0 = 0 N m^2/C [verified!]

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