Three long parallel wires A, B and C are perpendicular to the page, carrying equal currents I in the same direction. Wire B lies distance d from both A and C, with BA perpendicular to BC. Find the magnitude of force per unit length acting on B. [Image]
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Question

Three long parallel wires A, B and C are perpendicular to the page, carrying equal currents I in the same direction. Wire B lies distance d from both A and C, with BA perpendicular to BC. Find the magnitude of force per unit length acting on B. [Image]

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G1 Physics · Accepted Answer

Step 1: Current-carrying parallel wires attract when currents are in the same direction. Step 2: Force per unit length between each pair separated by d is f = μ₀I²/(2πd). Step 3: Forces on wire B from wires A and C have equal magnitudes f and are perpendicular because ∠ABC=90°. Step 4: Resultant force per length = √(f²+f²) = √2 f = μ₀I²/(√2 πd). Final answer: (D) μ₀I²/(√2 πd).