Two long parallel conducting wires carry currents of 30 A in opposite directions and are separated by 8 cm. What is the magnitude of the magnetic field at the midpoint between the wires? Take μ₀/4π = 10⁻⁷ N·A⁻².
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Question

Two long parallel conducting wires carry currents of 30 A in opposite directions and are separated by 8 cm. What is the magnitude of the magnetic field at the midpoint between the wires? Take μ₀/4π = 10⁻⁷ N·A⁻².

Options

G1 Physics · Accepted Answer

The midpoint is 4 cm = 0.04 m from each wire. Magnetic field due to one long straight wire is B = μ₀I ÷ (2πr). Because the currents are opposite, the magnetic fields at the midpoint point in the same direction and add. Therefore, B(total) = 2×μ₀I ÷ (2πr) = μ₀I ÷ (πr). Using μ₀ ÷ (4π) = 10⁻⁷, so μ₀ ÷ π = 4 × 10⁻⁷, B(total) = 4 × 10⁻⁷×30 ÷ 0.04 = 3.0 × 10⁻⁴ T = 300 μT. Correct option: B.