Two parallel long wires carry the same current and repel each other with a force F per unit length. If both these currents are doubled and the wire separation tripled, the force per unit length becomes:
Correct answer: D. 4F/3
- A. 2F/9
- B. 2F/3
- C. 4F/9
- D. 4F/3
Explanation
When the two parallel long wires carry the same current and repel each other with a force F per unit length we have:F₁ / ℓ = I² B μ₀ / (2 π h)And when the currents are doubled and the wire separation tripled, the force per unit length becomes:F₂ / ℓ = (2I)² B μ₀ / (2 π (3h))F₂ / ℓ = 4 I² B μ₀ / (2 π (3h))F₂ / ℓ = (4/3) I² B μ₀ / (2 π h) = (4/3) F₁ / ℓTherefore, when the currents are doubled and the wire separation tripled, the force per unit length becomes 4/3 of the initial force per unit length.
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