Assignment #1 (Due 9/5/01)

Griffiths: 1.4, 1.6, 1.10

Assignment #2 (Due 9/12/01)

Griffiths: 1.12, 1.15, 1.18, 1.21, 1.25, 1.29, 1.32

Assignment #3 (Due 9/19/01)

1.33, 1.37, 1.42, 1.46, 1.49

Assignment #4 (Due 9/26/01)

2.1, 2.4, 2.6

(Note: This assignment has been shortened. Some problems have been moved to next week!)

Assignment #5 (Due 10/3/01)

Griffiths 2.9, 2.13, 2.14, 2.17, 2.22, 2.26, 2.36

Assignment #6 (Due 10/10/01)*

Griffiths 3.2, 3.7, 3.10

More explicit instructions for 3.2:
In your own words, say how Earnshaw's theorem follows directly from Laplace's equation.
For the cube, write an expression for V(x,y,z). Try to show that the function has a local maximum by looking at the second derivative along some direction where a test charge is likely to leak out of the "bottle" if it can. (If you are having trouble proving it either way, you are probably on the right track.) Plot the potential along special directions using Mathematica, Maple or some other package to show that it is, in fact, NOT a stable equilibrium. Also, plot the second derivative along these directions.

Extended to 10/12/01!

Assignment #7 (Due 10/17/01)*

Griffiths 3.12, 3.14, 3.15, 3.17, 3.22

Assignment #8 (Due 10/31/01)*

Griffiths 3.26, 3.27, 3.33, 4.1, 4.6

Assignment #9 (Due 11/7/01)*

Griffiths 4.13, 4.16, 4.21, 4.22**, 4.23, 4.31

**The general solution for V in cylindrical coordinates can be calculated from separation of variables. It is an interesting problem, but we don't have time for everything, so I'll provide the general solution.

You might want to convince yourself that each term is in fact a solution to Laplace's Equation.

Assignment #10 (Due 11/16/01)*

Griffiths 5.2**, 5.4, 5.6, 5.9, 5.11

**For 5.2, sketch by hand or with a Math software package.

Assignment #11 (Due 11/21/01)*

Griffiths 5.14, 5.15, 5.25, 5.26

S1) A long straight wire has a circular cross section of radius R. Inside the conductor there is a cylindrical hole of radius a, whose axis is parallel to the axis of the wire and is offset by a distance b. The wire carries a current that has a uniform current density of J for the conductor. a) Show that the magnetic field inside the hole is uniform. b) Find the magnetic field on the axis of the conductor.
(Hint: You can treat the current density in the hole as the sum of two equal and opposite currents similar to the charges in Problem 2.1 or the polarizations in Problem 4.16.)

(Note: there have been two changes in the assignment. 5.31 has been moved to next week and 5.23 has changed to 5.25 since I did that one class)

Assignment #12 (Due 11/30/01)*

Griffiths 5.31, 5.35, 1.61(b), (c) and (e) (with the corresponding proofs from 1.60), 6.5, 6.8

Assignment #13 (Due 12/7/01)*

Griffiths 6.12, 6.17, 6.26, 7.7, 7.9, 7.11**

**For 7.11, you will need both the resistivity and the density of aluminum. The resistivity is 2.65x10^-8 ohm-meters. The density is 2.7x10^3 kg/m^3. Also, you need to assume a cross-sectional area, but this should not affect the final answer.

Assignment #14 (Due 12/14/01)*,**

Griffiths 7.15, 7.17, 7.20, 7.23, 7.24, 7.33***

**This whole assignment will be counted as bonus. However, you are responsible for the material so it is strongly suggested that you at least try all the problems and not just wait for the solutions.

*** This refers to problem 7.16, which was done in class.