24. Electric Force & Field; Gauss' Law

An infinitely wide, horizontal metal plate lies above a horizontal infinite sheet of charge with surface charge density 800 nC/m². The bottom surface of the plate has surface charge density -100 nC/m². What is the surface charge density on the top surface of the plate?

FIGURE P24.46 shows an infinitely wide conductor parallel to and distance d from an infinitely wide plane of charge with surface charge density η. What are the electric fields $\overrightarrow{E_A}$ to $\overrightarrow{E_D}$ in regions A to D?

A spark occurs at the tip of a metal needle if the electric field strength exceeds $3.0\times {10}^6$ N/C, the field strength at which air breaks down. What is the minimum surface charge density for producing a spark?

Figure 24.32b showed a conducting box inside a parallel-plate capacitor. The electric field inside the box is $\overrightarrow{E}=\overrightarrow{0}$. Suppose the surface charge on the exterior of the box could be frozen. Draw a picture of the electric field inside the box after the box, with its frozen charge, is removed from the capacitor. Hint: Superposition.