Home Work Set # 8, Physics 217, Due: November 7,
A point charge q is situated a large distance r from a
neutral atom of polarizability α. Find the force of attraction
A very long cylinder, of radius R
, carries a uniform polarization
perpendicular to its axis.
a) Find the electric field inside
b) Show that the field outside
the cylinder can be expressed
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).
1. Problem 3.
Find the electric field in all three regions by two different
a) First calculate the bound charges and then calculate the field
b) Use Gauss's law to find the electric displacement
and then get
there is no free
charge in the problem.
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
, and the axis is perpendicular to
Suppose you have enough linear dielectric material, of dielectric constant
K, to half-fill a parallel-plate capacitor (see Figure 2).
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?
2. Problem 5.