Question

In problem set #1, problem 1.4, how does one find that r dr = s ds? one would think that r ds = s dr. Thank you for any help!

Answer 1

\[s=\sqrt{r^{2}+z^{2}} \]
or,
\[s^2=r^2+z^2\]

here we know that z is a constant quantity. now, on differentiating it w.r.t. r (or s) we get
sds=rdr

Answer 2

So, \[s ds = rdr + zdz\]
where
\[zdz = 0\]
?

Answer 3

remember z is a constant,so dz=0

Answer 4

In question it is given that we have to fiind the quantity at z distance (it means z is fixed or constant).

But to solve the problem we are taking a ring at a distance r which can be varied from 0 to R. and since r is varied z have to vary.