Two long parallel wires carry currents of 5.0 A and 8.0 A in opposite directions. The wires are separated by 0.30 m. Find the magnetic force per unit length between the two wires.

Question

BlackTom AI · Accepted Answer

The magnetic force per unit length between two long, straight, parallel currents is given by F/L = (μ0 I1 I2) / (2π r).

1) Relevant knowledge points and concepts
- Biot–Savart/Lorentz law leads to the standard result for force per unit length between two long parallel currents: F/L = μ0 I1 I2 / (2π r).
- μ0 (the permeability of free space) = 4π × 10^−7 T·m/A.
- Two currents in opposite directions produce a repulsive force (parallel currents attract; anti-parallel repel).

2) Step-by-step reasoning
- Substitute the known values into the formula: I1 = 5.0 A, I2 = 8.0 A, r = 0.30 m, μ0 = 4π × 10^−7 T·m/A.
- Compute algebraically, simplifying π factors before numeric arithmetic to reduce rounding error.

3) Calculations with intermediate steps
F/L = (μ0 I1 I2) / (2π r)
= [(4π × 10^−7) × (5.0) × (8.0)] / [2π × 0.30]
Cancel π in numerator and denominator:
= [4 × 10^−7 × (5.0 × 8.0)] / [2 × 0.30]
Compute currents product: 5.0 × 8.0 = 40
Numerator: 4 × 10^−7 × 40 = 160 × 10^−7 = 1.60 × 10^−5
Denominator: 2 × 0.30 = 0.60
Divide: (1.60 × 10^−5) / 0.60 = 2.666... × 10^−5 ≈ 2.7 × 10^−5 N per meter

4) Why the correct answer is correct
- The numeric result follows directly from the standard formula and correct substitution/simplification. The sign/direction follows from the rule that anti-parallel currents repel, so the force is repulsive.

5) Why the other options are incorrect
- 7.2 × 10^−5 N values are too large by roughly a factor of ~2.7; they likely result from algebraic error (e.g., not using 2π in the denominator correctly or using μ0 = 4π×10^−6 instead of 4π×10^−7).
- The options labeled “attractive” are wrong because the currents are in opposite directions; opposite currents repel, not attract.

6) Conclusion
The magnetic force per unit length is 2.7 × 10^−5 N (repulsive), which matches the provided correct answer.

Two long parallel wires carry currents of 5.0 A and 8.0 A in opposite directions. The wires are separated by 0.30 m. Find the magnetic force per unit length between the two wires.单项选择题

类似问题

Two parallel conductors each of 0.50 m length, separated by 5 x 10-3 m and carrying 3.0 A in opposite directions, will experience what type and magnitude of mutual force? (magnetic permeability in empty space μ0 = 4π x 10-7 T m/A)

What was the world's first widely adopted biodiversity policy?

The aim of the Paris Agreement is to ensure that the earth’s preindustrial temperature is not exceeded by more than º Celsius.

The IPCC's mission is to Blank ______.

Why have most international agreements for environmental protection been based on the honor system?

As was exhibited with the Montreal Protocol and the encouragement of reduced CFC production, trade can be an effective tool to compel compliance with international treaties.

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单