Electric Fields in Conductors Practice Problems

An infinitely long nonconducting cylindrical shell with uniform charge density is coaxially enclosed by an infinitely long conducting cylinder of radius R, separated by a distance d as shown below. Determine the electric fields in regions I, II, III, and IV.

A thin film of silicon dioxide is used as an insulating layer for microelectronic devices. When the electric field perpendicular to the layer exceeds 9.1 x 10⁹ V/m, the material will undergo dielectric breakdown. Determine the minimum surface charge density on the oxide layer to trigger this breakdown.

A thin non-conducting rectangular sheet is placed over a metal plate having similar surface dimensions and a top surface charge density of 2.3 µC/m². What must be the surface charge density at the bottom surface of the metal plate if the non-conducting sheet has - 4.6  µC/m²?

Consider a conducting cuboid container placed between the two plates of a capacitor as shown. Assuming the charge on the outer layer of the container could be fixed, sketch a representation of the electric field within the container after it, along with its fixed charge, has been removed. The internal electric field of this container is denoted as E and equals zero.

A metal spherical ball of radius 5 cm carries a charge of 50 nC. Determine the electric field (E) at a distance of 0.01 cm from the outer surface of the ball.

A conducting solid sphere of radius 10 cm is charged by conduction with a positive rod. The sphere acquires a charge of 10 μC. Determine the electric field, E, at point A located just inside the sphere.