Question

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

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.

Short answer

Student 1 is accurate

Step-by-step solution

Given information and theory used 

Given students'arguments :

Student 1: Because spheres A and B contain equal charges, the fluxes across them are equal.

Student 2: However, on sphere B, the electric field is weaker than on sphere A. Because the flux is proportional to the strength of the electric field, the flux through A is greater than the flux through B.

Student 3: I thought we spoke about surface area when we talked about flux. Because sphere B is larger than sphere A, I believe the flow through B is greater than that through A.

Theory used :

The electric flux is defined as the amount of electric field that goes through a closed surface. According to Gauss's law, the electric flux across a surface is proportional to the charge inside the surface:

${\Phi }_e=\oint \overrightarrow{E}·d\overrightarrow{A}=\frac{Q_{in}}{{\epsilon }_0}$. ...(1)

Determining which of the students is correct

The electric flow is determined by the charge inside the closed surface. Based on equation (1), we can conclude that student 1 is correct because both spheres have the same charge.

Because the flux is given by $\Phi =EA$, Studies 2 and 3 are erroneous because, in order to maintain the flux constant, the electric field must fluctuate as well.