2. Jackson 7.2
3. Jackson 7.4
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Set 7 (due 11/20)
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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.
3.
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.
4.
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
t=0.
(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,
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Set 6:(due 11/1) problem 5.3; 5.6; 5.13
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Set 5 (due 10/11) probs 4.6; 4.8; 4.13
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Set 4 (due 9/27) prob. 3.17a,b; 3.20a
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Set 3 (due 9/20)
prob. 3.1; 3.3;
3.7
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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)
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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
p2.2
p2.23 (prob 2.13 in the second edition)
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