An isolated conductor has net charge$\mathbf{+}\mathbf{10}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{6}}\mathbf{}\mathbf{C}$ and a cavity with a particle of charge$\mathbf{=}\mathbf{+}\mathbf{3}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{6}}\mathbf{}\mathbf{C}$ What is the charge on (a) the cavity wall and (b) the outer surface?

Charge of uniform volume density $\mathbf{r}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{2}\mathbf{nC}\mathbf{/}{\mathbf{m}}^{\mathbf{3}}$ fills an infinite slab between role="math" localid="1657340713406" $\mathbf{x}\mathbf{=}\mathbf{-}\mathbf{5}\mathbf{.}\mathbf{0}\mathbf{}\mathbf{cm}$ and role="math" localid="1657340708898" $\mathbf{x}\mathbf{=}\mathbf{+}\mathbf{5}\mathbf{.}\mathbf{0}\mathbf{}\mathbf{cm}\mathbf{}\mathbf{.}$ What is the magnitude of the electric field at any point with the coordinate (a) $\mathbf{x}\mathbf{=}\mathbf{4}\mathbf{.}\mathbf{0}\mathbf{}\mathbf{cm}$ and (b) $\mathbf{x}\mathbf{=}\mathbf{6}\mathbf{.}\mathbf{0}\mathbf{}\mathbf{cm}$ ?

A particle of charge $\mathbf{1}\mathbf{.}\mathbf{8}\mathbf{\mu C}$ is at the center of a Gaussian cube $\mathbf{55}\mathbf{}\mathbf{cm}$ on edge. What is the net electric flux through the surface?

Two large metal plates of area $\mathbf{1}\mathbf{.}\mathbf{0}{\mathit{m}}^{\mathbf{2}}$ face each other, $\mathbf{5}\mathbf{.}\mathbf{0}\mathit{c}\mathit{m}$ apart, with equal charge magnitudes but opposite signs. The field magnitude $\mathbf{\left|}\mathbf{q}\mathbf{\right|}$ between them (neglect fringing) is 5N/C . Find $\mathbf{\left|}\mathbf{q}\mathbf{\right|}$ .

At each point on the surface of the cube shown in Fig. 23-31, the electric field is parallel to the z-axis. The length of each edge of the cube is $\mathbf{3}\mathbf{.}\mathbf{0}\mathbf{}\mathbf{m}$. On the top face of the cube the field is $\overrightarrow{\mathbf{E}}\mathbf{=}\mathbf{-}\mathbf{34}\hat{\mathbf{k}}\mathbf{}\mathbf{N}\mathbf{/}\mathbf{C}$ and on the bottom face it is $\overrightarrow{\mathbf{E}}\mathbf{=}\mathbf{+}\mathbf{20}\hat{\mathbf{k}}\mathbf{}\mathbf{N}\mathbf{/}\mathbf{C}$ Determine the net charge contained within the cube.

Space vehicles traveling through Earth’s radiation belts can intercept a significant number of electrons. The resulting charge buildup can damage electronic components and disrupt operations. Suppose a spherical metal satellite 1.3m in diameter accumulates $\mathbf{2}\mathbf{.}\mathbf{4}\mathbf{}\mathbf{\mu C}$ of charge in one orbital revolution. (a) Find the resulting surface charge density. (b) Calculate the magnitude of the electric field just outside the surface of the satellite, due to the surface charge.