Question

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

Short answer

I agree with student number two.

Step-by-step solution

Step 1. Given Information

The sphere and ellipsoid are depicted in the diagrams below.

Step 2. Which student you agree with

The following is a summary of the students' conversation.

Student 1 claims that flux is same because the average radius is the same.

Student 2 agrees that the fluxes are equivalent because they are both surrounded by the same charge.

Student 3 claims that because the flux is not perpendicular to B, flux via B is lower than flux through A.

Student 4 claims that Gauss's law does not apply to B, making comparison impossible.

The debate can be summarized as follows:

I agree with student number two.

Because the sphere and the ellipsoid both have the same charge q, the flux through both will be equal. The flow is determined by the charge encompassed by the surface, not by its shape.

Both the sphere and the ellipsoid encompass the same charge, resulting in equal fluxes.

I agree with student 2 that the same charge encased by both results in the same flux passing through them.