HW 4 results

Overall, I was very pleased with homework 4. The average was 91.4% (std. dev. 8.2%), and most questions had an average of 90% or better:


Questions 2 and 8 caused some trouble though. Question 2 was difficult, I think, due to the unusual phrasing of the problem. This was intentional - you were given realistic data that one could easily measure, and asked to deduce something you can't easily measure. It is a conceptually tricky problem, I think it may be worth your time to read through the solution to this one.

Question 8 was also conceptually tricky. Definitely have a look at the solutions for this one. Briefly:

a) Charge carrier density in a metal is determined mainly just by how many atoms per unit volume there are. Each atom contributes a certain number of mobile electrons, like in problem 4.

b) Current density is just current per unit area - if one doubles, so does the other

c) Drift velocity is proportional to current and the electric field, if current doubles, so does drift velocity.

d) The collision time was assumed to be a constant for each material because it is primarily determined by the random thermal velocity, not the drift velocity. Chaotic thermal motion which gives no net displacement dominates the carrier motion, drift velocity is a tiny effect that gives a small net motion in one direction. In our simple model, collision time depends only on temperature and materials properties.