Home Work Set # 8, Physics 217, Due: November 7,
2001
Problem 1
A point charge q is situated a large distance r from a
neutral atom of polarizability α. Find the force of attraction
between them.
Problem 2
A very long cylinder, of radius
R, carries a uniform polarization
perpendicular to its axis.
a) Find the electric field
inside the
cylinder.
b) Show that the field
outside the cylinder can be expressed
as
Problem 3
A thick spherical shell (inner radius a, outer radius b) is
made of dielectric material with a "frozen-in" polarization
where k is a constant and r is the distance from the center
(see Figure 1).
Figure
1. Problem 3.Find the electric field in all three regions by two different
methods:
a) First calculate the bound charges and then calculate the field
they produce.
b) Use Gauss's law to find the electric displacement
,
and then get
.
Note:
there is no
free charge in the problem.
Problem 4
A very long cylinder of linear dielectric material is placed in an
otherwise uniform electric field
.
Find the resulting field within the cylinder. (The radius is
R, the
susceptibility
χe, and the axis is perpendicular to
.)
Problem 5
Suppose you have enough linear dielectric material, of dielectric constant
K, to half-fill a parallel-plate capacitor (see Figure 2).
a)
By what fraction is the capacitance increased when you distribute the material
as shown in Figure 2a?
b) By what fraction is the capacitance increased when
you distribute the material as shown in Figure 2b?
Figure
2. Problem 5.
