PHY 712 -- Assignment #1
January 13, 2020
Read Chapters I and 1 and Appendix 1 in Jackson.
- Jackson Problem #1.5. Be careful to take into account the behavior of Φ(r) for r-->0.
PHY 712 -- Assignment #2
January 15, 2020
Continue reading Chap. 1 in Jackson.
- Using the Ewald summation methods developed in class, find the electrostatic interaction energy of a NaCl lattice having a cubic lattice constant a. Check that your result does not depend of the Ewald parameter η. You are welcome to copy (and modify) the maple file used in class. A FORTRAN code is also available upon request.
PHY 712 -- Assignment #4
January 22, 2020
Continue reading Chap. 1 in Jackson.
- For the two-dimensional rectangular system discussed in the lecture notes, work out the analytic form of the electrostatic potential Φ(x,y) for the Example #1 and #2 charge densities given on slide 16 of Lecture 4.
PHY 712 -- Assignment #6
January 27, 2020
Continue reading Chap. 2 in Jackson.
- Eq. 2.5 was derived as the surface change density on a sphere of radius a due to a charge q placed at a radius y > a outside the sphere. Determine the total surface charge on the sphere surface.
- Now consider the same system except assume y < a representing the charge q being placed inside the sphere. What is the surface charge density and the total surface charge in this case?
PHY 712 -- Assignment #7
January 29, 2020
Continue reading Chap. 2 and 3 in Jackson.
- Consider the example of the long cylindrical charge distribution discussed in Lecture 7. Verify the solutions given on slide 10 for this case. (Note: extra points awarded for correcting mistakes on the slides.)
PHY 712 -- Assignment #8
January 31, 2020
Complete reading Chapter 3 and start Chapter 4 in Jackson .
- Consider the charge density of an electron bound to a proton in a hydrogen atom -- ρ(r) = (1/πa03) e-2r/a0, where a0 denotes the Bohr radius. Find the electrostatic potential Φ(r) associated with ρ(r). Compare your result to HW#1.
PHY 712 -- Assignment #9
February 3, 2020
Continue reading Chapter 4 in Jackson .
- Work problem 4.9(a) in Jackson, evaluating the coefficients of the spherical harmonic terms.
PHY 712 -- Assignment #10
February 7, 2020
Start reading Chapter 5 in Jackson .
- Consider an infinitely long cylindrical wire with radius a,
oriented along the z axis. There
is a steady uniform current inside the wire. Specifically, in terms of
r the radial parameter of the cylindrical coordinates of the system
the current density is J(r)=J0 , where
J0 is a constant vector along the z-axis,
for r ≤ a and zero otherwise.
- Find the vector potential (A) for all r.
- Find the magnetic flux field (B) for all r.
PHY 712 -- Assignment #11
February 10, 2020
Continue reading Chapter 5 in Jackson .
- In class we "derived" the electron-nucleus hyperfine interaction. Evaluate the expectation value of this interaction for two different cases for an electron in an eigenstate of hydrogen atom with quantum numbers nlmms with n=2, l=0, m=0, ms=1/2 and with n=2, l=1, m=0, ms=1/2. In both cases assume that the proton spin is mps=1/2
PHY 712 -- Assignment #12
February 12, 2020
Finish reading Chapter 5 in Jackson .
- Work through the details of the magnetic shielding example given in Section 5.12 of your textbook. Verify Eqs. 5.121 and 5.122.
PHY 712 -- Assignment #14
February 17, 2020
Finish reading Chapter 6 in Jackson .
- Supply the details of the derivation of Eq. 6.105 in Jackson from Eq. 6.104.
- Supply the details of the derivation of Eq. 6.121 in Jackson from Eq. 6.114.
PHY 712 -- Assignment #15
February 19, 2020
Continue reading Chapter 7 in Jackson .
- Consider the reflectivity of a plane polarized electromagnetic wave
incident from air (n=1) on a material with refractive index
n'=1.5 at an angle of incidence i, Plot the reflectance
R(i)=|E"0/E0|2
as a function of i for 0 ≤ i ≤ 90 deg for both cases of polarization of (E0 in the plane of incidence or perpendicular to the plane of incidence). What is the qualitative difference between the two cases?
PHY 712 -- Assignment #16
February 21, 2020
Finish reading Chapter 7 in Jackson .
- Work problem 7.22 (a) in Jackson.
PHY 712 -- Assignment #17
March 23, 2020
Start reading Chapters 9 in Jackson .
- Work problem 9.10(b) in Jackson.
PHY 712 -- Assignment #19
March 27, 2019
Finish reading Chapters 9 and 10 in Jackson .
- Work problem 9.16(a) in Jackson. Note that you can use an approach similar to that discussed in Section 9.4 of the textbook, replacing the "center-fed" antenna with the given antenna configuration.
PHY 712 -- Assignment #20
March 30, 2020
Begin reading Chapter 11 in Jackson .
- Derive the relationships between the component of the electric and magnetic field components E1, E2, E3, B1, B2, and B3 as measured in the stationary frame of reference and the components E'1, E'2, E'3, B'1, B'2, and B'3 measured in the moving frame of reference. Note that the reverse relationships are given in Eq. 11.148.
PHY 712 -- Assignment #21
April 03, 2020
Continue reading Chapter 11 in Jackson .
- Supply some of the intermediate steps for deriving the E and B fields resulting from a particle of charge q moving along the x-axis at constant speed v, measured at a point a distance b along the y-axis.
PHY 712 -- Assignment #22
April 6, 2020
Continue reading Chap. 14 in Jackson .
- Consider an electron moving at constant speed βc ≈ c in a circular trajectory of radius ρ. Its total energy is E= γ m c2. Determine the ratio of the energy lost during one full cycle to its total energy. Evaluate the expression for an electron with total energy 400 GeV in a synchroton of radius ρ=103 m.
PHY 712 -- Assignment #23
April 13, 2020
Finish reading Chap. 14 in Jackson .
- Compare Eq. 14.79 in Jackson with the corresponding expression given in the lecture notes. Are they equivalent?
PHY 712 -- Assignment #24
April 15, 2020
Finish reading Chap. 14 and start Chap. 15 in Jackson .
- Derive the Compton formula given on page 696 of Jackson.