E&M, Fall '10, Homework 5

Problems based (mostly) on UP Chapter 26

1. Problem 1 ("coulombs and electrons")

2. Problem 8 ("A wire")

3. Problem 26 ("100 W lightbulb")

4. Problem 40 ("truncated right circular cone")

5. Recall, from the last chapter, Equation (25-16) which expresses the potential difference between two points in terms of a path integral from one point to another. It is kind of tacitly assumed that this integral depends only on the endpoints -- not on the particular path chosen to connect them. (Otherwise, given a potential at point 1, you could assign different values to the potential at point 2, and there would sort of cease to be any meaningfully-defined potential field at all.) Anyway, starting with the statement that the path integral of E is path-independent, derive the statement that the curl of E vanishes. (Note this problem has almost nothing to do with what we've done in this course so far; it's just a kind of check-in to see where you're at with the vector calc stuff.)