Solve Current in Parallel Wires with Repulsion

[Touchme]

Homework Statement

Two long parallel wires, each with a mass per unit length of 43 g/m, are supported in a horizontal plane by 6.0 cm long strings, as shown in Figure P19.64. Each wire carries the same current I, causing the wires to repel each other so that the angle between the supporting strings is 16°.
Determine the magnitude of each current.

Homework Equations

sin (theta) = opposite/hyp

I^2 = [(2pi)(d)(mg/L)] / [(4pi)e-07]

The Attempt at a Solution

First I found d (the distance between the wires). Which is 2[sin(8)](0.06m) = 0.0167m.
Then I substitute the given into this equation: I^2 = [(2pi)(d)(mg/L)] / [(4pi)e-07]. I = sq.root of [(2pi)(0.0167)(0.043)(9.8)] / [(4pi)e-07]. the answer I got is 132.64 A. What did I do wrong?

I tried using free body diagram.
T = mg/sin8
Tcos8 = [(I^2)(L)((4pi)e-7)] / [(2pi)d]
(mgcos8)/(sin8) = [(I^2)(L)((4pi)e-7)] / [(2pi)d]
(mg/L)(7.115) = [(I^2)((4pi)e-7)] / [(2pi)0.0167]
I = 159.8 A

Still incorrect.

 

[Touchme]

Ah shoot, I've made the most stupid mistake ever. I solved it.

 

[m2003]

I would like to point out that the given information and equations may not be sufficient to accurately determine the magnitude of the current in this scenario. Additional information such as the tension in the strings and the distance between the wires at equilibrium would be needed to solve for the current using the equations provided. It is also important to consider the effects of gravity and the magnetic field on the wires in this setup. Further experimentation and calculations may be necessary to accurately determine the current in this parallel wire system.