Homework 4 Solutions
Physics 721
Spring 2013
1
Jackson 4.2
A point dipole with dipole moment p is located at the point x0 . From the properties of the derivative of a
Dirac delta function, show that for calculation of the potential or the energy of a dipo
Homework 7 Solutions
Physics 721
Spring 2013
1
Jackson 7.4
A plane-polarized electromagnetic wave of frequency in free space is incident normally on the at surface
of a nonpermeable medium of conductivity and dielectric constant .
(a)
Calculate the amplit
Homework 2 Solutions
Physics 721
Spring 2013
1
Jackson 1.10
Prove the mean value theorem: For charge-free space the value of the electrostatic potential at any point is
equal to the average of the potential over the surface of any sphere centered on that
Homework 5 Solutions
Physics 721
Spring 2013
1
Jackson 5.3
A right-circular solenoid of nite length L and radius a has N turns per unit length and carries a current I.
Show that the magnetic induction on the cylinder axis in the limit N L is
Bz =
0 N I
(c
Homework 6 Solutions
Physics 721
Spring 2013
1
Jackson 6.1
In three dimensions the solution to the wave equation (6.32) for a point source in space and time (a light
ash at t = 0, x = 0) is a spherical shell disturbance of radius R = ct, namely the Green
Midterm 1 Solutions
Physics 721
Spring 2013
1
Two conducting spheres of radius a, one charged and the other neutral, are placed distance d a apart.
Find the force between the spheres, if the chage on the rst sphere is Q.
The neutral sphere will be plarize
Homework 1 Solutions
Physics 721
Soring 2013
1
Jackson 1.3
Using Dirac delta functions in the appropriate coordinates, express the folowing charge distributions as
three-dimensional charge densities (x).
The equations to use in solving this problem are
f
Homework 8 Solutions
Physics 721
Spring 2013
1
Jackson 8.14
Consider an optical ber with a graded index of refraction for rays conned to the x z plane, n(x) =
n(0) sech(x). The ber has large enough transverse dimensions (x) to contain all rays of interest
Homework 3 Solutions
Physics 721
Spring 2013
1
Jackson 3.3 (a)
A thin, at, conducting, circular disc of radius R is located in the x y plane with its center at the origin,
and is maintained at a xed potential V . With the information that the charge densi