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Two parallel conductors lie in the plane of the paper, separated by a distance X₀. A charged particle travels with velocity v between these wires, maintaining a distance X₁ from one of them. When both wires carry identical currents I flowing in the same direction, the particle's trajectory has a curvature radius of R₁. Conversely, if the currents in the wires flow in opposite directions, the curvature radius becomes R₂. Given that X₁/X₀ equals 3, determine the ratio R₁/R₂.
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Correct answer: 3
Solution
When the currents in the wires flow in the same direction, the magnetic forces on the particle add up, resulting in a smaller radius of curvature (R₁). When the currents flow in opposite directions, the forces partially cancel, leading to a larger radius (R₂). The ratio R₁/R₂ is determined to be 3 based on the geometry and current configuration.
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