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?

A spark occurs at the tip of a metal needle if the electric field strength exceeds 3.0 x 10⁶ 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 E (→ above E) = 0 (→ above 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.

A charged paint is spread in a very thin uniform layer over the surface of a plastic sphere of diameter 12.0 cm, giving it a charge of −49.0 μ C. Find the electric field (b) just outside the paint layer;