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Two very long, parallel wires are separated by d = 0.015 m. The first wire carries a current of I1 = 0.25 A. The second wire carries a current of I2 = 0.15A.

Randomized Variables d = 0.015 m
I1 = 0.25 A
I2 = 0.15 A Part (a) Express the magnitude of the force between the wires per unit length, f, in terms of I1, I2, and d.
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Part (b) Calculate the numerical value of f in N/m.
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Part (c) Is the force repulsive or attractive?
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Part (d) Express the minimal work per unit length needed to separate the two wires from d to 2d.
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Part (e) Calculate the numerical value of w in J/m.
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Explanation / Answer

a)

we know, F = mue*I1*I2*L/(2*pi*d)

F/L = mue*I1*I2*/(2*pi*x)

b)

F/L = 4*pi*10^-7*0.25*0.15/(2*pi)

= 7.5*10^-9 N/m

c) attrcative

d)

work done per unit length = integral (F/L)*dx ( x is from d1 to d2)


= intrgral mue*I1*I2*/(2*pi*x) * dx

= mue*I1*I2*/(2*pi) *ln(x) ( x is from d1 to d2)


= mue*I1*I2*/(2*pi) *ln(d2/d1)


= mue*I1*I2*/(2*pi) *ln(2*d/d)

= mue*I1*I2*ln(2)/(2*pi)


e)
= 4*pi*10^-7*0.25*0.15*ln(2)/(2*pi)

= 5.198*10^-9 J/m

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