Jackson 1.1 Homework Problem Solution
Dr. Christopher S. Baird
University of Massachusetts Lowell
PROBLEM:
Use Gauss's theorem S En da=
q
and Ed l=0 to prove the following:
0
a) Any excess charge placed on a conductor must lie entirely on its surface. (A
Jackson 2.2 Homework Problem Solution
Dr. Christopher S. Baird
University of Massachusetts Lowell
PROBLEM:
Using the method of images, discuss the problem of a point charge q inside a hollow, grounded,
conducting sphere of inner radius a. Find
(a) the pot
Jackson 2.5 Homework Problem Solution
Dr. Christopher S. Baird
University of Massachusetts Lowell
PROBLEM:
(a) Show that the work done to remove the charge q from a distance r > a to infinity against the force,
Eq. (2.6), of a grounded conducting sphere i
Jackson 2.4 Homework Problem Solution
Dr. Christopher S. Baird
University of Massachusetts Lowell
PROBLEM:
A point charge is placed a distance d > R from the center of an equally charged, isolated, conducting
sphere or radius R.
(a) Inside of what distanc
Jackson 2.3 Homework Problem Solution
Dr. Christopher S. Baird
University of Massachusetts Lowell
PROBLEM:
A straight-line charge with constant linear charge is located perpendicular to the x-y plane in the first
quadrant at (x0, y0). The intersecting pla
Jackson 2.7 Homework Problem Solution
Dr. Christopher S. Baird
University of Massachusetts Lowell
PROBLEM:
Consider a potential problem in the half-space defined by z 0, with Dirichlet boundary conditions on
the plane z = 0 (and at infinity).
(a) Write do
Jackson 2.9 Homework Problem Solution
Dr. Christopher S. Baird
University of Massachusetts Lowell
PROBLEM:
An insulated, spherical, conducting shell of radius a is in a uniform electric field E0. If the sphere is cut
into two hemispheres by a plane perpen
Jackson 2.12 Homework Problem Solution
Dr. Christopher S. Baird
University of Massachusetts Lowell
PROBLEM:
Starting with the series solution (2.71) for the two-dimensional potential problem with the potential
specified on the surface of a cylinder of rad
Jackson 2.11 Homework Problem Solution
Dr. Christopher S. Baird
University of Massachusetts Lowell
PROBLEM:
A line charge with linear charge density is placed parallel to, and a distance R away from, the axis of
a conducting cylinder of radius b held at f
Jackson 2.1 Homework Problem Solution
Dr. Christopher S. Baird
University of Massachusetts Lowell
PROBLEM:
A point charge q is brought to a position a distance d away from an infinite plane conductor held at
zero potential. Using the method of images, fin
Jackson 1.9 Homework Problem Solution
Dr. Christopher S. Baird
University of Massachusetts Lowell
PROBLEM:
Calculate the attractive force between conductors in the parallel plate capacitor (Problem 1.6a: area A,
separated by distance d) and the parallel c
Jackson 1.2 Homework Problem Solution
Dr. Christopher S. Baird
University of Massachusetts Lowell
PROBLEM:
The Dirac delta function in three dimensions can be taken as the improper limit as 0 of the
Gaussian function
[
D ; x , y , z = 2 3/ 2 3 exp
]
1
x
Jackson 1.3 Homework Problem Solution
Dr. Christopher S. Baird
University of Massachusetts Lowell
PROBLEM:
Using Dirac delta functions in the appropriate coordinates, express the following charge distributions as
three-dimensional charge densities (x).
(a
Jackson 1.5 Homework Problem Solution
Dr. Christopher S. Baird
University of Massachusetts Lowell
PROBLEM:
The time-averaged potential of a neutral hydrogen atom is given by
r
=
qe
4 0 r
1
r
2
where q is the magnitude of the electronic charge, and -1 = a
Jackson 1.4 Homework Problem Solution
Dr. Christopher S. Baird
University of Massachusetts Lowell
PROBLEM:
Each of three charged spheres of radius a, one conducting, one having a uniform charge density within
its volume, and one having a spherically symme
Jackson 1.6 Homework Problem Solution
Dr. Christopher S. Baird
University of Massachusetts Lowell
PROBLEM:
A simple capacitor is a device formed by two insulated conductors adjacent to each other. If equal and
opposite charges are placed on the conductors
Jackson 1.7 Homework Problem Solution
Dr. Christopher S. Baird
University of Massachusetts Lowell
PROBLEM:
Two long, cylindrical conductors of radii a1 and a2 are parallel and separated by a distance d, which is
large compared with either radius. Show tha
Jackson 1.8 Homework Problem Solution
Dr. Christopher S. Baird
University of Massachusetts Lowell
PROBLEM:
(a) For the three capacitor geometries in Problem 1.6 calculate the total electrostatic energy and express
it alternatively in terms of the equal an
Jackson 1.10 Homework Problem Solution
Dr. Christopher S. Baird
University of Massachusetts Lowell
PROBLEM:
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
Jackson 2.13 Homework Problem Solution
Dr. Christopher S. Baird
University of Massachusetts Lowell
PROBLEM:
(a) Two halves of a long hollow conducting cylinder of inner radius b are separated by small
lengthwise gaps on each side, and are kept at differen