Lecture 1, Jan 21, 99

Review of electrostatics: Coulomb's law, relation of field to potential, E = - ÑV. Charge distribution on insulators and conductors.

Assigned reading (by next Thursday): Bloomfield, section 11.1

Assigned problem set 1

References:

• Tipler, chapters 18 and 19, or Serway, chapters 16 and 17 or equivalent (review);
• PQRG, section 5.3.3 (Electrostatics) and review of section 8.17.5 (Differential Operators);

Problem session 1

Given hints on solving problem set 1, using MAPLE to do the plots. Handed out MAPLE help sheet.

Lecture 2, Jan 26

Continued review of electrostatics: Ñ × E = 0, Ñ · E = r/e₀ (or Ñ · E = 4pr in gaussian units) and Poisson's equation ѲV = - r/e₀ (or ѲV = - 4pr in gaussian units). In charge-free space (Laplace's equation). Analogy of electric field to fluid velocity for an incompressible, non-viscous fluid. Dipole moment; field of a dipole, force on a dipole (proportional to field gradient). Induced dipole on a conducting sphere and on a molecule. Electrical discharges.

References:

• Tipler, chapters 20 and 21;
• 311 Lecture Notes, Fluid Mechanics Preliminaries, especially the problem of flow past a cylinder in Drag and D'Alambert's paradox (review)

Lecture 3, Jan 28

Demos: discharges from domes and a sharp point; Jacob's ladder (effect of previous discharges); precipitating smoke particles.

The electric potential of a dipole of strength p pointing in the z direction is V_dip = k pz/r³, where k = 1/4pe₀ in SI (k = 1 in gaussian units).
This can be rewritten as V_dip = k pcosq/r², where q is the angle from the z axis.
If a conducting sphere of radius a is placed in a uniform electric field E₀, a dipole moment p = (1/k)E₀ a³ is induced on the sphere. A uniform field in the z direction is described by the potential V₀ = - E₀ z. The total potential for the sphere in the uniform field is then

V_tot = V₀ + V_dip = - E₀ z + E₀ za³/r³, for r > a (outside the sphere) and V_tot = 0 for r < a (inside the sphere). The two expressions for V_tot match for r = a (on the surface of the sphere), as they must.
It is also true that V_tot = 0 on the plane z = 0. This means that V_tot is also the solution for the problem of homework 2, a hemispherical boss in a conducting plane.

Assigned problem set 2.

References:

• Feynman, section II - 6-4 for the dipole field
• Generally, chapters II-1 to II-12 of Feynman correspond to chapters 18 to 21 of Tipler, but are at a higher level.
• David J. Griffiths, Introduction to Electrodynamics:
  - Inside cover: vector derivatives
  - p. 89-91: Electrostatic boundary conditions
  - p. 116-118: Uniqueness theorem for electrostatics
  - Example 8, p. 141-142: Conducting sphere in a uniform electric field

Problem session 2

Solutions to problem set 1. Given hints on solving set 2 and getting pretty plots with MAPLE. See example at http://erwin.phys.virginia.edu/~jsf9k/hints.html. See also MAPLE short course notes, on reserve.

Lecture 4, Feb 2

Demos: shown "insides" of electrostatic air cleaner and laser printer.

Uniqueness of solution of Laplace's equation, , with assigned vaues of V on the boundary (in practice, V has assigned values on various conductors). How to proceed if the charges on the conductors are given, instead of the values of the potential. Simplest example: Q = C(V₁ - V₂) for a capacitor with charges +Q and -Q on the plates at potentials V₁ and V₂. C is the capacitance.

Started review of quantum theory:

What is quantized and when? In periodic motion, action is quantized in units of h; as a consequence, other quantities are quantized too, but not so simply.
What is action? It is a quantity with dimensions ML²T^-1; it can be energy × time, or momentum × length. Angular momentum has the same dimensions as action and is simply quantized in units of .
What is spin? It is something like the internal angular momentum of an elementary particle. However, electrons (and quarks) have spin /2, while orbital angular momentum must be an integer multiple of . Photons have spin . One often says that electrons have spin 1/2 and photons have spin 1.
What is the Pauli exclusion principle? Read about it in Serway, page 860, or Tipler, page 1206 and 1234, as it applies to electrons. Actually, it applies to all elementary particles with spin 1/2 (called fermions) and is mysteriously related to their unusual spin. It also applies to composite particles with half-integer spin (1/2, 3/2, etc.).

References:

• For capacitances: Tipler, chapter 21 ; PQRG, page 91; Serway, pages 480 - 495.
• For quantum mechanics: Tipler, chapter 35, or Serway, chapter 29.
• A readable review of the early history and basic concepts of quantum theory is found in the sections on "Atoms" and on "Particles and Waves" of Fowler's notes for Phys 252.

Note however that these references use Planck's constant h instead of , so that some formulas look a little different. Physics articles today almost always use , unless they use "atomic units" in which is set equal to 1. See last semester's lecture on atomic units.
Phys 252 lectures are at www.phys.virginia.edu/classes/252.
The Phys 311 lecture is at www.phys.virginia.edu/classes/311/notes/units/node2.html

Lecture 5, Feb 4

Review of quantum mechanics: action, phase, sum over all possible paths with a phase factor, uncertainty principle, spin and the Pauli exclusion principle, plane wave solution of the time-dependent Schrodinger equation, E = hf = w and p = k.

Assigned problem set 3 (engineering of electrostatic precipitator, basic quantum theory).