A schedule of content and exercises will appear gradually below.
Homework is due before the start of the Tuesday lecture of the
following week, unless noted otherwise. Please hand in either at the
lecture or directly to Glen
Burella.
Week 1:
Notes:
We gave an overview of the material to be
covered and reviewed some of the material from MP231 (chapters 1 through
8 of the notes
by Charles Nash)
Notes:
We introduced the concept of Electromotive Force (EMF) as well as
Faraday's induction law.
Part of this material is covered in Chapter IX,
paragraph 1 of the notes
by Charles Nash
Exercises:
Please find assignment 1 here.
The solutions to assignment 1 are available here
In addition, there are some very useful exercises made up by Glen Burella
here.
These exercises don't have to be handed in, but are very useful and will
be covered in tutorials, so please do as many as possible.
Week 4:
Notes:
We derived the continuity equation for
electric charge and introduced Maxwell's fourth equation (the one
involving the curl of the magnetic
field).
Part of this material is covered in Chapter IX,
paragraphs 2 and 3 of the notes
by Charles Nash
Week 5:
Notes: We introduced electromagnetic waves. Starting from
Maxwell's equations without charge or current density, we derived wave
equations for the coponents of the electric and magnetic fields and
studied the properties of the solutions, for unidirectional waves. We then
used the Maxwell equations to derive that unidirectional electromagnetic
waves are transversal and that their magnetic fields are determined by
their electric fields (and vice versa).
Exercises:
Please find assignment 2 here.
The solutions to assignment 2 are available here
Week 6:
We looked more specifically at electromagnetic plane waves. We noted again
that the waves are transversal, that the E and B field are orthogonal to each
other and that B is determined by E through Maxwell's equations (and vice
versa). We had an overview of the electromagnetic spectrum by
wavelength and frequency and we introduced the concept of polarization.
Week 7:
Notes:
We introduced the energy density and the Poynting vector (the energy
current density) and we proved the Poynting theorem, which is the
continuity equation for the energy in the electromagnetic fields when no
charges are present, or more generally, the equation which expresses
conservation of energy in terms of the energy
density, the Poynting vector and the work performed on charged particles.
We also calculated the energy density and Poyhting vector in some examples
involving electromagnetic waves
Exercises:
Please find assignment 3 here.
The solutions to assignment 3 are available here
Week 8:
Notes:
We finished off the "Electricity and Magnetism" part of the course with
some final words on polarization of waves (linear and circular
polarization in particular) and with some more examples of energy density
and flow (power dissipated in wire, power stored in capacitor), using the
Poynting vector.
We also just about managed to start the "Statistical Thermodynamics" part
of the course. If you feel like you could do with a reminder of the
various forms of the ideal gas law, please look at these exercises for practice with the ideal
gas law
Week 9:
Notes:
We introduced microstates and macrostates of a gas, the ideal gas law and
the Maxwell-Boltzmann velocity distribution. In the tutorial, we
calculated the normalisation of the Maxwell-Boltzmann distribution and
most likely speed.
in the following lecture, we started on the derivation of the
Maxwell-Boltzmann velocity distrubution, first fixing its general form and
then fixing the remaining parameters by expressing the pressure of the
gas and the number of particles in terms of integrals involving the
distribution.
This material is covered in sections 1 and 4 of
the Notes on Statistical Mechanics
by Prof. Nash.
Almost all of the material covered in these notes was eventually
covered by this course, so read them!
Exercises:
Please find assignment 4 here.
The solutions to assignment 4 are available here
Week 10:
Notes: We finished the derivation of the
Maxwell-Boltzmann velocity distrubution, analogous to that given in
paragraph 1 of the Notes on
Statistical Mechanics by Prof. Nash. We introduced the necessary
integrals on the way. We also calculated the average kinetic energy
of a gas molecule and compared a number of typical speeds for the gas -
the root mean square velocity (see section 2 of the notes), the most
likely velocity (section 4 and assignment 4) and the average speed of a
gas molecule (this was calculated in the lecture but is not in Prof.
Nash's notes - the main point to make is that it turns out to be of the
same order of magnitude as the root mean square velocity and most likely
speed).
Week 11:
Notes:
We introduced the equipartition theorem and applied it to the
specific heats of gases and solids. This material is treated in sections 2
and 3 of the notes. We also introduced the mean free path of a gas
molecule (see section 5 of the notes).
Exercises:
Assignment 5 is available from Glen or Joost or from the table in the
Mathematical Physics department (if there are any left)
The solutions to assignment 5 are available here (with thanks to Glen)
Week 12:
Notes:
We gave an estimate for the electrical conductivity, based on our estimate
of the mean free path and on an estimate of the drift velocity of the
molecules in the gas (see notes section 5 - the treatment in the
lecture made some slightly different estimates, but everything comes out
in the same order of magnitude). We finished with some considerations on
quantum corrections (see notes section 6), arguing basically that quantum
corrections set in at low temperatures, where the quantitative
meaning of "low" depends on the density or pressure of the gas.
Exercises:
Assignment 6 is an old exam, please find it here.
This assignment will be treated in the review tutorial.