24. Electric Force & Field; Gauss' Law

Given three closed Gaussian surfaces as shown in Figure 1, each enclosing different charge distributions, which of the following statements correctly describes the relationship between the net electric flux $\Phi$ through a surface and the net charge $Q$ enclosed by that surface according to Gauss' Law?

If the figure shows a closed Gaussian surface enclosing a net charge $Q$, what is the total electric flux $\Phi$ through the surface according to Gauss’ Law?

Which of the following Gaussian surfaces will have a total electric flux of $0$ according to Gauss' Law?

In Gauss's law, the total electric flux through a closed surface is equal to which of the following quantities?

Why is symmetry useful when applying $Gauss’slaw$ to calculate electric fields?

According to Gauss' Law, how should the integral $∯E_n\ast dA$ be evaluated?

Charge $q$ is distributed uniformly throughout the volume of an insulating sphere of radius $R=4.00$ cm. At a distance of $r=8.00$ cm from the center of the sphere, the electric field due to the charge distribution has magnitude $E=940$ N/C. What is the volume charge density for the sphere?

Rank the flux through surfaces A, B and C in the figure below from greatest to smallest.

A spherical, thin conducting shell of radius 8cm has a charge of –6C. If a 4C charge were placed at the center of the shell, what is the electric field 4 cm from the center? At 12 cm?

The nuclei of large atoms, such as uranium, with $92$ protons, can be modeled as spherically symmetric spheres of charge. The radius of the uranium nucleus is approximately $7.4\times10^{-15}$ m. The electrons can be modeled as forming a uniform shell of negative charge. What net electric field do they produce at the location of the nucleus?