For Friday September 2, 2005

• 1.11 a) and b)
• Problem 1.4
• Problem 1.5

• 1.21 a) and b)
• 1.24 a)
• Find sqrt(130), by writing 130 = 121+9 = 121 (1+9/121) and using the binomial expansion, including the leading term and one other. Compare this to the answer from your calculator.

• Find the electric field on the axis of a hollow cylindrical shell a distance D from the center of the shell along the shell's axis. The shell has a radius R and length L. There is a uniform charge per unit area on the shell's curved surface.
• Ditto except that the cylinder of radius R and length L has a uniform charge per unit volume.

• 2.9
• 2.16
• 2.17 (started in class)
• 2.18 (hard)
• 2.21 (electric potential)
• 2.27 (electric potential)

• 2.32
• 2.33
• 2.34
• 2.38
• 3.2 Find V(x) where x is distance on the x-axis of the cube. Plot V vs. x and show a particle at the center will not be confined

• Griffiths 3.13. Use 200 terms. Let Vo = 4 Pi volts, and a = 1 m. Plot sigma over the range y=0 to 1 m, in unit of C/m^2.  Indicate what you did in Maple, but don't turn in maple output other than a couple of lines and the graph.
• Solve Griffiths' 3.14 for Vo = 1000 v and a = 1.00 m using the averaging technique with a grid of 100 x 100 in Excel, over the range 0 to 1 m in both x and y.
• Solve Griffiths' 3.14 analytically ( Vo = 1000 v,  a = 1 m, b = 1 m) with the series method of section 3.3. Evaluate V numerically at x = 1/2 m, y = 1/2 m, z = any in Maple using 10 nonzero terms in x and 10 nonzero terms in y. Compare your answer to that of the previous problem.
• For the previous problem, estimate how many terms in the series you might need at x=0.1 m, y = 1/2 m, and at x=0.9 m, y = 1/2 m.  Support your estimate with a calculation in one or both of these cases.
• Griffiths' 3.15.  Just write out the series in compact form.
• Griffiths' 3.33. I suggest you take the negative gradient of V, starting with the x-component, then assemble the result into a vector like the one Griffiths gives, a form not dependent on x, y and z.

• Text 4.15, p. 177
• Text 4.18, p. 184
• Text 4.19, p. 185
• Text 4.20, p. 185
• Text 4.32, p. 198
• Extra Credit. Calculate the quadrupole moment of an axisymmetric ellipsoid of total charge Q bounding surface (x/a)^2 + y(/a)^2 + (z/b)^2 = 1. Q = integral [ rho dV (2z^2-x^2-y^2) ] The answer should come out in terms Q, a and b. [See Great Ellipsoid Trick.]

• Text 5.9, p. 219
• Text 5.25, p. 239
• Text 5.46, p. 249 (Helmholtz coils)
• a) Show that B on the axis of a long solenoid at the end is equal to just half that in the middle. [ Hint: put two identical solenoids together, so they act like a single one.]
• b) Find B on the axis of a solenoid of current I, length L with N turns, and radius R, at a distance d from one end. [We did a solenoid calculation and integrated in class to show B inside is mu_o nI. Try modifying that calculation.]
• Text 5.55. Remember that z^ = r^ cos theta - theta^ sin theta. [Don't spend too much time on this one  unless you see what to do.]

For Friday November 4, 2005

• Turn in an analysis of your data for the Earth's magnetic field. The ballpark is around 1/4 gauss.

• Griffith's 9.16, p. 392
• Calculate the reflection coefficient R, as called for on p. 7 of the notes
• Calculate T based on the alternative formulation of the normal incidence problem, with Er reversed.

1. (10) Work out the transmission coefficient for a layer of thickness a and index n2 between two media of index n1 and n3. Show that when the layer thickness a is 1/4 wavelength (or odd 1/4 wavelength) and the index of the layer is the geometrical mean of the other two (n_2^2 = n_1 n_3) that the transmission coefficient becomes 1. (This is a non-reflecting coating.)  You may follow the work on the 6-page handout from 11/7/05 called 'Reflection and Refraction', especially pages 3-6. But you must put the work together yourself. Quoting a result from the handout will not do; you must start from the beginning and go to the end, complete with sketches of the waves.

2. (10) Assume a magnetization M = 8.3 x 10^5 A/m and calculate the B field at the surface of a disc of thickness 3 mm and radius 9 mm. i) (5)  First, be simple-minded and pretend it is at the center of a circular current loop. ii) (5) Then treat it as a shallow solenoid.