Homework assignment
set 8. (due 12/4)
1. In this exercise you will calculate the pressure due to a plane wave when it is reflected from
   a planar surface.  Consider the case that the electric field of the plane wave is polarized parallel to the
   plane of incident. The incident angle is theta.
   (a) the elementary method.
         Calculate the momentum of the incident plane wave. Calculate the change of momentum when the
       incident wave is reflected. From this calculate the pressure.
   (b) Use the formula involving the Maxwell stress tensor.
         Calculate the electric and magnetic field near the planar surface. The follow the definition to
         obtain the pressure which is the diagonal component of the Maxwell stress tensor.

2.  Jackson 7.2
 3. Jackson 7.4

Set 7 (due 11/20)
1. Problem 6.8  of Jackson
see the following guide to work out this problem.
         Start with the equation derived in problem 6.7 where you can find the B field due
  to a moving electric dipole polarization. The last term can be treated as an effective
  magnetization. If you can prove that the curl of H is zero, then you can use the scalar
  magnetic potential concept. From (5.100)   you then can prove the equation given,
  Calculate the B and H vectors inside the dielectric.

2.   A current I flows through a resistor R in the form of a long
    straight wire. Show that the poynting vector flows radially inward through
    the surface of the wire with the correct magnitude to  produce the Joule heating.

This problem is adopted from the book of Heald and Marion, 4-12 and 4-13. It
is a good exercise of manipulating the time-dependent Maxwell equations.

   Consider a parallel-plate capacitor consisting of two circular plates. The radius of
the plate is a and the plate separation is h and the medium is filled with a dielectric which
has dielectric constant $\ipsilon$. The capacitor is charged by connecting to a battery
with EMF V_0 and a series resistor R. If the circuit is closed at t=0 find the following
quantities within the capacitor as a function of time. Neglect the edge effect.
(a) The electric field.
(b)  the magnetic field.
(c) the Poynting vector.
(d) the total field energy.
(f) the scalar potential.
(g) the vector potential.

Continue problem 3, but now assume that the material between the plates have
conductivity $\sigma$ in addition to being a dielectric.  Forget the resistor in problem
w2. This capacitor is charged to a potential V_0 by a battery and then disconnected at
(a) Find the free charge on the capacitor as a function of time.
(b)  Find the conduction current, the displacement current density.
(c) Find the magnetic field H within the capacitor,


Set 6:(due 11/1)  problem 5.3; 5.6; 5.13
Set 5 (due 10/11)  probs 4.6;  4.8; 4.13

Set 4 (due 9/27) prob. 3.17a,b; 3.20a

Set 3 (due 9/20)
prob.    3.1;    3.3;     3.7
Problem set 1.   Jackson pp50-52  (due 8/28)

    1.1;   1.3;   1.5;    1.6a,b;  1.9  (identical problems in the 2nd edition)

Problem set 2, (due 9/6)
These are just exercises.
e1.  Derive eq. (2.5). Perform the numerical integration to find the fraction
of the induced charge on the front half facing the fixed charge q. Use the
two parameters in Fig. 2.3.

e2. Show that the force is indeed given by eq. (2.9).
       For Q=2q, at what y will the force becomes attractive.

e3. From eq. (2.15) calculate the dipole moment from the induced surface
   charge and show that the result is identical to the dipole moment from the
   two image chages.

e4. Eq. (2.20) cannot be integrated analytically. This exercise requires you to
write a program to do numerical integration. Note that the problem has
cyclindrical symmetry so the answer does not depend on the azimuthal angle.
Calculate the potential for x ranges from a to 10a and theta from 0 to pi.
Present your results in a surface plot or a contour plot.

Note: The equation numbers are the same as in the 2nd edition.

problems from Jackson, chapter 2


p2.23 (prob 2.13 in the second edition)