S8 Covariant Electromagnetism

Overall an apparently satisfactory paper, producing a range of marks from 5 
to 49 out of a possible 50, with a mean in a sensible place. Of the various
groups taking the paper, the number of second years is too small to make
generalisations. However the third-year physics and philosophy students made
up exactly half the  candidates and can be considered separately. This group
produced both the maximum and minimum marks referred to, and also a worryingly
large proportion of the very weak scripts.

Question 1 (Covariance of electromagnetism under Parity)

One of the aims of this paper is to cover quite a lot of new theoretical 
ground, which precludes developing problem-solving skills. The style of this
first question reflects this emphasis, giving candidates the opportunity 
to discuss covariance in a specific case (Parity) without any significant 
calculation. However very few candidates realised that, whereas for the 
position vector of an object P(\vec r)=-\vec r, if we view \vec r as a field 
then P(\vec r)=+\vec r. All the relevant ideas were found in the answers as 
a whole, and in some cases all on the same script, but never with any 
coherence, and no answers came very close to full marks.

Question 2 (Lorentz transformation of electromagnetic potentials)

This question was very straightforward and lacked a sting in the tail, so that
it was popular and many candidates got nearly full marks. It was reassuring
to see that many candidates had grasped the central idea of this option and
were able to transform a field from one reference frame to another.

Question 3 (Covariant equation of motion of a charged particle in a field)

This question produced the full range of marks from 2 to 25, but many
candidates did not do well. A small number ignored the hint in the question and
attempted the more powerful but difficult eigenvalue method to solve the
differential equations, which was generally beyond them. Some candidates were
quite unable to solve differential equations at all, and a surprising number
thought that velocity was part of a four-vector. The question was in fact a
very easy question disguised in a relativistic framework, but the disguise was
perhaps too effective.

Question 4 (Gauge-invariance of non-relativistic quantum mechanics)

Although it was the least popular question on the paper, it was in fact an
easy question because all the syllabus-related facts were contained in the
question. As a result candidates could obtain over half marks just by following
the instructions in the question, and three of the eight attempts were of very
high quality.

C W P Palmer