Assignment 11

Problem 1:

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?

Problem 2:

A satellite has a polar orbit about the earth with a radius of 5.49*106 m above the earth's surface.  On one orbit it passes over Greenwich at 0o longitude and 51.48o latitude. Approximately where will it pass over exactly one orbit later?  The radius of the earth is RE = 6.38*106 m and its mass is 5.98*2024 kg.

Problem 3:

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).

imageProblem 4:

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?


Problem 5:

Two earth-like planets, each with mass m = 6*1024 kg, orbit each other in a circular orbit once every 50 days.  Find the distance between their centers in km.