Repulsion and deflection of current Two long, straight parallel wires hang from

Question

Repulsion and deflection of current

Two long, straight parallel wires hang from strings of length 10 cm from a common point on a ceiling. The wires carry the same current, I, and repel each other with enough force that their strings make an angle of 10 degree to the vertical. Each of the long wires has a mass equal to 20 g per meter of length. Given the repulsion between the wires, are the currents through the two wires parallel or anti-parallel? Determine the value of I needed to cause this deflection.

Explanation / Answer

Here ,

let the tension in the cable is T

Now, balancing the forces

distance between wires , d = 2 * sin(10 degree) * 0.10

d = 0.0347 m

a)

for repulsion ,the current in the wires is anti parallel

b)

Now , for the value of I

tan(10) = 4pi *10^-7 * I^2/(2pi * 0.0347 * 0.020 * 9.8)

solving for I

I = 77.4 A

the current in the wires is 77.4 A

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