Lecture (30 minutes)
- Derive expression on the board for the potential due to a finite line.
- What coordinate system should we choose?
- What is the charge density?
- Physics sense-making about result
- Break into groups, talk about what sense-making you would do without doing it; groups should have a list and should definitely have more than one or two things.
- Check dimensions (overall and combined).
- Functional behavior
- Does it get smaller as I get farther away from the line (in both directions)?
- Limiting cases (power series)
- What happens if you shrink the line to no height but keep the charge constant
- What happens if you get really close to the line?
- What if the line is infinite? (This is a longish lecture and a bit more sophisticated than much of the other material. It is an excellent opportunity to do lots of series expansions and review logarithm rules. Alternatively, it can be left out to save time.)
