How Do Magnetic Field Lines Behave Around a Long Current-Carrying Wire?

[Fumbles22]

Hello,

I'm stuck on this question, and it's really annoying me. I scanned the page so it has a bit more context.

It's question 3.7: "A long wire carrying a steady current is placed in a uniform magnetic field parallel to it's own length. What is the shape of the magnetic field lines close to the wire?".

I approached the problem like this:

(Sorry about my awful handwriting!)

I'm close to the answer in the back of the book (which i'll withhold for now) but it still isn't right. Unfortunately, I can't see what I've done wrong.

I was hoping that someone could point out any gaps in my working.

Thanks in advance!

 

[rude man]

I don't see what's wrong with what you did. Maybe you could express r as sqrt(x^2 +y^2) but other than that ...

 

[njoysci]

refer to example problem 31.14 for the derivation
http://teacher.pas.rochester.edu/phy122/Lecture_Notes/Chapter31/chapter31.html