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

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Fumbles22
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Hello,

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

Figure 3.14: two arrow maps of magnetic field lines around a long straight wire, (a) current flowing away from the viewer shown as concentric circles with arrows, (b) current flowing towards the viewer shown with a dot-in-circle symbol.


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:

Handwritten notes on lined paper deriving the magnetic field B(r) of a current-carrying wire plus a uniform field A along x, with a sketch of circular field loops around the wire.


(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!
 
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