Homework assignment

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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

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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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