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The wires repel each other with some force.
The magnitude of this force can be given by
F=
Il
×
B
where l is length of wire
B=
2πr
μ
∘
I
where r is distance between two wires
r=2Lsinθ
F=
2π2Lsinθ
μ
∘
I
2
l
...(i)
Now the tension in the thread is keeping both wire from moving to sideways
From FBD of the wire
Tsinθ=F...(ii)
Tcosθ=mg...(iii)
dividing equation (ii) by (iii)
tanθ=
mg
F
m=λL
I=2sinθ
μ
∘
cosθ
πλgL
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