The net electric flux through each face of a die (singular of dice) has a magnitude in units of ${\mathbf{10}}^{\mathbf{3}}\mathbf{}{\mathbf{Nm}}^{\mathbf{2}}\mathbf{/}\mathbf{C}$ that is exactly equal to the number of spots N on the face (1 through 6). The flux is inward for N odd and outward for N even. What is the net charge inside the die?

Flux and conducting shells. A charged particle is held at the center of two concentric conducting spherical shells. Figure 23-39ashows a cross section. Figure 23-39b gives the net flux $\mathbf{\varphi }$ through a Gaussian sphere centered on the particle, as a function of the radius rof the sphere. The scale of the vertical axis is set by $\mathbf{\varphi }\mathbf{=}\mathbf{5}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{5}}{\mathbf{m}}^{\mathbf{2}}\mathbf{/}\mathbf{C}$ .What are (a) the charge of the central particle and the net charges of (b) shell A and (c) shell B?

Figure 23-23 shows, in cross section, a central metal ball, two spherical metal shells, and three spherical Gaussian surfaces of radii R, 2R, and 3R, all with the same center. The uniform charges on the three objects are: ball, Q; smaller shell, 3Q; larger shell, 5Q. Rank the Gaussian surfaces according to the magnitude of the electric field at any point on the surface, greatest first.

The electric field just above the surface of the charged conducting drum of a photocopying machine has a magnitude E of $\mathbf{2}\mathbf{.}\mathbf{3}\mathbf{\times }{\mathbf{10}}^{\mathbf{5}}\mathbf{}\mathbf{N}\mathbf{/}\mathbf{C}$ . What is the surface charge density on the drum?

Figure 23-52 gives the magnitude of the electric field inside and outside a sphere with a positive charge distributed uniformly throughout its volume. The scale of the vertical axis is set by ${\mathit{E}}_{\mathbf{s}}\mathbf{=}\mathbf{5}\mathbf{.}\mathbf{0}\mathbf{\times }\mathbf{10}\mathit{N}\mathbf{/}\mathit{C}$ . What is the charge on the sphere?

Figure 23-55 shows two non-conducting spherical shells fixed in place on an x-axis. Shell 1 has uniform surface charge density $\mathbf{+}\mathbf{4}\mathbf{.}\mathbf{0}\mathbf{\mu C}\mathbf{/}{\mathbf{m}}^{\mathbf{2}}$ on its outer surface and radius $\mathbf{0}\mathbf{.}\mathbf{50}\mathbf{}\mathbf{cm}$ , and shell 2 has uniform surface charge density on its outer surface and radius $\mathbf{2}\mathbf{.}\mathbf{0}\mathbf{}\mathbf{cm}$ ; the centers are separated by $\mathbf{L}\mathbf{=}\mathbf{6}\mathbf{.}\mathbf{0}\mathbf{}\mathbf{cm}$ . Other than at $\mathbf{x}\mathbf{}\mathbf{=}\mathbf{\infty }$, where on the x-axis is the net electric field equal to zero?