Need help coming up with dl in cylindrical coords.

[vwishndaetr]

The whole problem consists of several parts, but my issue is to come up with a dl for the piece of wire shown.

Im trying to find the force on the wire due to a magnetic field produced by another wire running along the x-axis (not shown in pic).

\vect{B} = \frac{\mu_0I}{2\pi s}\hat{\phi}

I am trying to get my dl x B so I can integrate, but I cannot come up with a dl. The reason I'm having trouble is because I know in cylindrical, for dl, both phi hat and s hat change along integration path for dl.

Someone please help I think I've tried every method except for the one that works. :(

 

[Delphi51]

I'm interested in this. It seems to me you need to use
B = μI/(2πr) = μI/(2πy) for the magnetic field at height y caused by the wire running along the x-axis. And for the force on the wire, wouldn't you just use
F = ILB or dF = IBdL ? You would then have to express dL as (cos θ)*dx to get an element of length perpendicular to B.