Find the Current using Force/Length Between Two Wires

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SUMMARY

The discussion centers on calculating the current in two parallel wires using the formula for the force per unit length between them. The given parameters include a separation distance of 0.006 m and a force of 8 μN acting on a 3 m length of one wire. The correct calculation reveals that the greater of the two currents is 0.40 A, achieved by correctly applying the equation F/L = (μ0)(Ia)(Ib) / 2∏d with μ0 set at 4∏ x 10^-7. A common mistake noted was the incorrect use of the distance value, where 0.06 m was mistakenly applied instead of the correct 0.006 m.

PREREQUISITES
  • Understanding of electromagnetic force between parallel conductors
  • Familiarity with the formula F/L = (μ0)(Ia)(Ib) / 2∏d
  • Basic algebra skills for solving equations
  • Knowledge of the physical constants involved, such as μ0
NEXT STEPS
  • Review the derivation of the force between parallel wires in electromagnetism
  • Practice solving problems involving multiple currents and forces
  • Explore the implications of wire separation on electromagnetic force
  • Investigate applications of Ampère's Law in real-world scenarios
USEFUL FOR

Physics students, electrical engineers, and anyone studying electromagnetic theory will benefit from this discussion, particularly those focusing on current calculations in parallel conductors.

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Homework Statement


Two long parallel wires are separated by .006 m. The current in one of the wires is twice the other current. If the magnitude of the force on a 3m length of one of the wires is equal to 8μN, what is the greater of the two currents?

The answer: .40 A

Homework Equations


F/L = (μ0)(Ia)(Ib) / 2∏d
μ0 = 4∏x10^-7
d = distance between the wires
Ia/b = values for the two currents

The Attempt at a Solution


I plugged everything in like so: (8x10^-6)/3 = (4∏x10^-7)(I)(2I)/2∏(.06)
From that, I divided the left side and the right, leaving me with:
2.67x10^-6 = 3.33x10^-6(2I^2)
Then I just solved for I by getting I by itself (.801/2 = I^2) and and taking the square root of (.801/2) to find I. At this point, I've found that I = .63A , but I don't know where to go from here. The answer should come out to be .40A.

 
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The problem says d = 0.006m but you used d = 0.06m
 

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