24. Electric Force & Field; Gauss' Law

A hollow, conducting sphere with an outer radius of $0.250$ m and an inner radius of $0.200$ m has a uniform surface charge density of $+6.37\(\times\)10^{-6}$ C/m². A charge of $−0.500$ $\(\mu\)$C is now introduced at the center of the cavity inside the sphere. What is the electric flux through a spherical surface just inside the inner surface of the sphere?

An infinite slab of charge is centered in the xy-plane. It has charge density $\rho ={\rho }_0{e}^{-\mid z\mid /z_e}$, where ρ₀ and z₀ are constants. This is a charge density that decreases exponentially as you move away from z = 0 in either the positive or negative direction. Find the electric field strength at distance z from the center of the slab.

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?

A very large, horizontal, nonconducting sheet of charge has uniform charge per unit area $\sigma =5.00\times {10}^{-6}$ C/m². A small sphere of mass $m=8.00\times {10}^{-6}$ kg and charge $q$ is placed $3.00$ cm above the sheet of charge and then released from rest. If the sphere is to remain motionless when it is released, what must be the value of $q$?

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\(\times\)10^{-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?

Charges $q_1=-4Q$ and $q_2=+2Q$ are located at $\text{𝓍}=-a$ and $\text{𝓍}=+a$, respectively. What is the net electric flux through a sphere of radius $2a$ centered (a) at the origin and (b) at $\text{𝓍}=2a$?

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?

The three parallel planes of charge shown in FIGURE P24.44 have surface charge densities ─ ½ η , η , and ─ ½ η. Find the electric fields $\overrightarrow{E_A}$ to $\overrightarrow{E_D}$ in regions A to D. The upward direction is the + y-direction.

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?

FIGURE EX24.2 shows a cross section of two concentric spheres. The inner sphere has a negative charge. The outer sphere has a positive charge larger in magnitude than the charge on the inner sphere. Draw this figure on your paper, then draw electric field vectors showing the shape of the electric field.

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

A conductor with an inner cavity, like that shown in Fig. $22.23$c, carries a total charge of $+5.00$ nC. The charge within the cavity, insulated from the conductor, is $-6.00$ nC. How much charge is on (a) the inner surface of the conductor and (b) the outer surface of the conductor?

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