PHY4324/Fall 09: EM II
HOMEWORK ASSIGNMENT #2:
due by 11:45 p.m. Friday 09/11
Instructor: D. L. Maslov
maslov@phys.ufl.edu 392-0513 Rm. 2114
Please help your instructor by doing your work neatly. Every (algebraic) final result
must be supplemented by a check of units. Without such a check, no more
than 75% of the credit will be given even for an otherwise correct solution.
1. At t = 0, the plates of a capacitor (capacitance C) are connected via a resistor (resistance R). Find the time
dependence of the charges on the plates. [25 points]
2. G7.3a [25 points]
3. G7.8 [25 points]
4. G7.10 [25 points]
5. Bonus: Coulomb Drag: Before Michael Faraday discovered the effect now bearing his name in 1831, there had
been many unsuccessful attempts to find mutual influences of d c currents. After Faraday’ discovery, everyone
got busy with ac currents and dc ones were forgotten. In 1989, however, a group at IBM [1] found an effect
which pre-Faraday physicists had been looking for. Shortly thereafter, a group at Bell Labs [2] repeated the
experiment in a somewhat different fashion, which is easier to describe. In a nutshell, here is a setup of the
Bell Labs experiment. Two parallel planes of a two-dimensional electron gas (although this is not entirely true,
think of one plane as an atomically thin conducting layer) are separated by a thin (0.1 µm) insulating layer.
When a dc current is passed through one of the planes, a much smaller dc occurs in the second plane.
a) What is your explanation of this effect? (Hint: think about the Coulomb interaction between electrons in
different layers.) [10 points]
b) If the dc field applied to one the planes is E0 , the mean free time for scattering electrons in different planes
at impurities is τi , and the mean free time with respect to scattering of electrons in different planes at each
other is τ , what is the induced electric field in the other plane? [10 points]
c) Why is the induced current so small that it required technology of the late XXth century to detect it?
[10 points]
[1] [P. M. Solomon, P. J. Price, D. J. Frank, and D. C. La Tulipe, New phenomena in coupled transport between 2D and 3D
electron-gas layers, Phys. Rev. Lett. 63, 2508 (1989).
[2] T. J. Gramila, J. P. Eisenstein, A. H. MacDonald, L. N. Pfeiffer, and K. W. West, Mutual friction between parallel twodimensional electron systems, Phys. Rev. Lett. 66 1216 (1991).
I
E0
FIG. 1: Problem 5
2D electron gases