Two long and parallel straight wires A and B carrying currents of 10 A and 4 A in the same direction are separated by a distance of 2 cm. Estimate the force on a 4 cm section of wire A. (μ₀=4π×10⁻⁷ SI)

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Accepted Answer

(2) 1.6×10⁻⁵ N. Given: I₁=10 A in A and I₂=4 A in B, same direction, separation d=2 cm=0.02 m; the section is ℓ=4 cm=0.04 m. Idea: wire B makes a field (μ₀I₂)/(2π d) at A, and A carries I₁ through it, so F=(μ₀I₁I₂ℓ)/(2π d). Force per unit length: F/ℓ=(2×10⁻⁷×10×4)/(0.02)=4×10⁻⁴ N m⁻¹. For the 4 cm section: F=4×10⁻⁴×0.04=1.6×10⁻⁵ N. The currents run the same way, so this force is an attraction towards B.

Two long and parallel straight wires A and B carrying currents of 10 A and 4 A in the same direction are separated by a distance of 2 cm. Estimate the force on a 4 cm section of wire A. (μ₀=4π×10⁻⁷ SI)

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