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 0.20 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.

Explanation / Answer

The field is oriented along one of the coordinate axes.

The flux through the four sides of the cube that are parallel to the field is zero.

The flux through the bottom of the cube is - E A

where E is the magnitude of the field

and A is the area of one side of the cube.

The flux through the top of the cube is + E A.

The net flux through the cube is EA - EA = 0 as expected.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.