In the following link is the
plan for the homework problem covering the entire semester in case you want to
plan ahead. It also contains the important information about the sections of
each chapter that we will study.
Full list of homework problems
More specifically, this is
the information of the homework problems, week by week:
Week 1: 1.
2.
3. Show that Eq. (1.17) (page 35,
top) satisfies the Poisson equation by following
the “a-potential”
procedure described on page 35. This
problem illustrates
how to carry out rigorous
mathematical proofs in the E&M context, where the
singular function
1/|x-x’| appears often in the calculation.
Week 2: 1.
2.
3.
that we will have in the
homework, thus make sure you understand how
to deal with these
functions.
Week 3: In 1,2,3 below (obviously!) you have to
provide more detail than in the book:
1. Show that Eq.(2.11) is correct, starting at Eq.(2.10)
2. Show that Eq.(2.14) is
correct, starting at Eq.(2.12).
3. Show that Eq.(2.22) is correct, starting at Eq.(2.19).
4. Jackson 2.23, only (a) (this is the only “new” problem)
Week 4: 1.
2. Show that Eq. (3.36) of
Sec.3.3 is correct, starting with the general formula Eq. (3.35).
Arriving to the first two
terms of Eq. (3.36) is sufficient.
3.
Week 5: 1,
2.
Week 6: no homework this week, because of first
mid-term exam
Week 7: 1.
2.
3. Starting with Eq. (5.14) in
the book, derive in detail Eq. (5.22).
4. Starting with Eq. (5.10) in
the book, show that for two long, parallel,
straight wires, carrying
currents I1 and I2, the force is attractive (repulsive)
if the currents flow in the
same (opposite) directions.
Week 8: 1.
2.
point is to see if Bz and Hz
are or not continuous at the interface.
3. Do the math that I skipped
in a lecture: show that taking the curl of
Eq. (5.55) you do get Eq.
(5.56).
Week 9: 1. Following the
steps in the book pages 210 and 211, show that (5.141)
is correct starting with
(5.136), namely show that k=1. This equation
includes the case in which
the surface S is changing with time (not
covered in class).
2. Show that the time-averaged
power input per unit volume is given
by (5.169), starting with
the expressions for the current and electric
field a few lines above.
3. This one is about the mathematics of
Chapter 6. Show that the current
J can be written as the sum
of the longitudinal current and the transverse
Current given by (6.27) and
(6.28).
Week 10: 1. In class, I explained (or tried to
explain) problem “Example 15” of
is about a current flowing
down a wire and the calculation aims
to find the energy per unit
time delivered to the wire using the
Poynting vector. Repeat
carefully the solution of the problem as in
book where the same result
“VI” is obtained by a more canonical
procedure.
2.
3.
4. Following the steps in
sphere is considered and
the force on the northern hemisphere
caused by the southern
hemisphere is calculated. In the third edition
of the book this example is in page
353, and the equation that you
are asked to show that it
is correct is Eq.(8.27).
Week 11: For the time being, just one problem since
I am aiming to having
the second mid-term exam this coming week. The problem
is:
1.
Week 12: 1.
2.
Week 13: 1.
2.
That was the last homework
of the semester!!