Problem 1.91 A cube is placed so that one corner is at the origin and three edge

Question

Problem 1.91

A cube is placed so that one corner is at the origin and three edges are along the x-, y-, and z-axes of a coordinate system (the figure (Figure 1) ). Use vectors to answer the questions.

Part A

Find the angle between the edge along the z-axis (line ab) and the diagonal from the origin to the opposite corner (line ad).

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Part B

Find the angle between line ac (the diagonal of a face) and line ad.

Problem 1.91

A cube is placed so that one corner is at the origin and three edges are along the x-, y-, and z-axes of a coordinate system (the figure (Figure 1) ). Use vectors to answer the questions.

Part A

Find the angle between the edge along the z-axis (line ab) and the diagonal from the origin to the opposite corner (line ad).

SubmitMy AnswersGive Up

Part B

Find the angle between line ac (the diagonal of a face) and line ad.

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.

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