Two infinitely long parallel wires A (current I) and B (current 2I) carry current in the same direction. Wire A has mass per unit length λ and rests on an insulated floor. Wire B is held directly above it at height h. Find the minimum allowed h for wire A not to lift. (μ₀ is vacuum permeability.)
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Question

Two infinitely long parallel wires A (current I) and B (current 2I) carry current in the same direction. Wire A has mass per unit length λ and rests on an insulated floor. Wire B is held directly above it at height h. Find the minimum allowed h for wire A not to lift. (μ₀ is vacuum permeability.)

Options

G1 Physics · Accepted Answer

Step 1: Force per unit length between parallel currents a distance h apart is f/L = μ₀I₁I₂/(2πh). Step 2: Here I₁ = I and I₂ = 2I, so upward magnetic attraction per unit length is μ₀I²/(πh). Step 3: Weight per unit length of wire A is λg downward. Step 4: To avoid lift-off, magnetic attraction must not exceed λg: μ₀I²/(πh) ≤ λg. Step 5: Solve for height: h ≥ μ₀I²/(πλg). Final answer: h(min) = μ₀I²/(πλg) (Option B).