6.4 Conductors in Electrostatic Equilibrium

How will the system above change if there are charged objects external to the sphere?

Under electrostatic conditions, the excess charge on a conductor resides on its surface. Does this mean that all the conduction electrons in a conductor are on the surface?

The conductor in the preceding figure has an excess charge of $– 5. 0 \mu \text{C}$. If a $2.0 - \mu \text{C}$ point charge is placed in the cavity, what is the net charge on the surface of the cavity and on the outer surface of the conductor?

Two parallel plates 10 cm on a side are given equal and opposite charges of magnitude $5.0 \times 10^{−9} \text{C} .$ The plates are 1.5 mm apart. What is the electric field at the center of the region between the plates?

A solid cylindrical conductor of radius a is surrounded by a concentric cylindrical shell of inner radius b. The solid cylinder and the shell carry charges +Q and –Q, respectively. Assuming that the length L of both conductors is much greater than a or b, determine the electric field as a function of r, the distance from the common central axis of the cylinders, for (a) $r < a ;$ (b) $a < r < b ;$ and (c)$r > b .$

Repeat the preceding problem, with $\overset{\rightarrow}{\text{E}} = 2 x \hat{i} + 3 x^{2} \hat{\text{k}} .$

A fellow student calculated the flux through the square for the system in the preceding problem and got 0. What went wrong?

Two $10 \text{cm} \times 10 \text{cm}$ pieces of aluminum foil of thickness 0.1 mm face each other with a separation of 5 mm. One of the foils has a charge of $+\text{30} \mu \text{C}$ and the other has $− 30 \mu \text{C}$. (a) Find the charge density at all surfaces, i.e., on those facing each other and those facing away. (b) Find the electric field between the plates near the center assuming planar symmetry.

The Hubble Space Telescope can measure the energy flux from distant objects such as supernovae and stars. Scientists then use this data to calculate the energy emitted by that object. Choose an interstellar object which scientists have observed the flux at the Hubble with (for example, Vegahttp://adsabs.harvard.edu/abs/2004AJ....127.3508B), find the distance to that object and the size of Hubble’s…