Solve Current in Parallel Wires with Repulsion

AI Thread Summary
The discussion revolves around calculating the current in two parallel wires that repel each other due to the same current flowing through them. The wires, each with a mass per unit length of 43 g/m, are suspended by strings at an angle of 16°. The initial attempt to find the current using the equation I^2 = [(2pi)(d)(mg/L)] / [(4pi)e-07] resulted in an incorrect value. After further analysis and using a free body diagram, the correct current was determined to be 159.8 A. The participant ultimately resolved their confusion and arrived at the correct solution.
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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.
 

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