A dielectric sphere with dielectric constant
K of radius R has a free charge density ρ distributed
uniformly throughout the volume.

(a) What is the electrostatic potential at
the center of the sphere, relative to infinity?

(b) How much energy is required to establish
this configuration, starting with the charge dispersed at
infinity?

A satellite has a polar orbit about the earth with a radius of 5.49*10^{6}
m above the earth's surface. On one orbit it passes over Greenwich at 0^{o}
longitude and 51.48^{o} latitude. Approximately where will it pass over
exactly one orbit later? The radius of the earth is R_{E} =
6.38*10^{6} m and its mass is 5.98*20^{24} kg.

The space between the plates of a parallel-plate capacitor is
filled with two slabs of linear dielectric material. Each slab has
thickness s, so the total distance between the plates is 2s. Slab 1 has a
dielectric constant of 2, and slab 2 has a dielectric constant of 1.5. The
free charge density on the top plate is σ and on the bottom plate −σ.
(The top plate is touching slab 1.)

(a) Find the electric displacement **D** in each slab.

(b) Find the electric field **E** in each slab.

(c) Find the polarization **P** in each slab.

(d) Find the potential difference between the plates.

(e) Find the location and amount of all the bound charge.

(f) Now that you know all the charge (free and bound), recalculate the
field in each slab, and compare with your answer to (b).

A satellite is in a circular orbit of radius r around an airless spherical planet of radius R. An asteroid of equal mass falls radially towards the planet, starting at zero velocity from a very large distance. The satellite and the asteroid collide inelastically and stick together, moving in a new orbit that just misses the planet's surface. What was the radius r of the satellite's original circular orbit in terms of R?

Two earth-like planets, each with mass m = 6*10^{24 }kg, orbit each
other in a circular orbit once every 50 days. Find the distance between
their centers in km.