Suppose you have the uniformly charged cube in FIGURE Q24.1. Can you use symmetry alone to deduce the shape of the cube’s electric field? If so, sketch and describe the field shape. If not, why not?

FIGURE Q24.1

FIGURE Q24.2 shows cross sections of three-dimensional closed surfaces. They have a flat top and bottom surface above and below the plane of the page. However, the electric field is everywhere parallel to the page, so there is no flux through the top or bottom surface. The electric field is uniform over each face of the surface. For each, does the surface enclose a net positive charge, a net negative charge, or no net charge? Explain.

FIGURE Q24.2

The square and circle in FIGURE Q24.3 are in the same uniform field. The diameter of the circle equals the edge length of the square. Is ${\text{Φ}}_{\text{square}}$ larger than, smaller than, or equal to ${\text{Φ}}_{\text{circle}}?$ Explain.

FIGURE Q24.3

In FIGURE Q24.4, where the field is uniform, is the magnitude of ${\text{Φ}}_{\text{A}}$ larger than, smaller than, or equal to the magnitude of ${\text{Φ}}_{\text{B}}$? Explain.

FIGURE Q24.4

What is the electric flux through each of the surfaces in FIGURE Q24.5? Give each answer as a multiple of $q\text{/}{ϵ}_0$.

FIGURE Q24.5

What is the electric flux through each of the surfaces A to E in FIGURE Q24.6? Give each answer as a multiple of $q\text{/}{ϵ}_0$.

FIGURE Q24.6

The charged balloon in FIGURE Q24.7 expands as it is blown up, increasing in size from the initial to final diameters shown. Do the electric field strengths at points 1, 2, and 3 increase, decrease, or stay the same? Explain your reasoning for each.

FIGURE Q24.7

The two spheres in FIGURE Q24.8 surround equal charges. Three students are discussing the situation.

FIGURE Q24.8

• Student 1: The fluxes through spheres A and B are equal because they enclose equal charges.

• Student 2: But the electric field on sphere B is weaker than the electric field on sphere A. The flux depends on the electric field strength, so the flux through A is larger than the flux through B.

• Student 3: I thought we learned that flux was about surface area. Sphere B is larger than sphere A, so I think the flux through B is larger than the flux through A.

Which of these students, if any, do you agree with? Explain.

The sphere and ellipsoid in FIGURE Q24.9 surround equal charges. Four students are discussing the situation.

FIGURE Q24.9

• Student 1: The fluxes through A and B are equal because the average radius is the same.

• Student 2: I agree that the fluxes are equal, but that’s because they enclose equal charges.

• Student 3: The electric field is not perpendicular to the surface for B, and that makes the flux through B less than the flux through A.

• Student 4: I don’t think that Gauss’s law even applies to a situation like B, so we can’t compare the fluxes through A and B.

Which of these students, if any, do you agree with? Explain.

A small, metal sphere hangs by an insulating thread within the larger, hollow conducting sphere of FIGURE Q24.10. A conducting wire extends from the small sphere through, but not touching, a small hole in the hollow sphere. A charged rod is used to transfer positive charge to the protruding wire. After the charged rod has touched the wire and been removed, are the following surfaces positive, negative, or not charged? Explain.

1. The small sphere.

2. The inner surface of the hollow sphere.

3. The outer surface of the hollow sphere.

FIGURE Q24.10