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AP Physics C: E&M
12.3 Magnetic Fields of Current-Carrying Wires and the Biot-Savart Law
12.2 Magnetism and Moving Charges
IntermediateMCQMathematicalProportional Analysis19.4k
A horizontal dashed reference line shows three circular wire cross-sections in the plane of the page. On the far left, a circle represents Wire 1, labeled Wire 1 with a centered dot indicating current directed out of the page and labeled I. On the far right, a circle represents Wire 2, labeled Wire 2 with an identical centered dot and labeled I. A horizontal double-headed dimension arrow extends between Wire 1 and Wire 2, labeled d. Between them on the dashed line, a third circle represents the mobile wire, also containing a centered dot and labeled I. A horizontal dimension arrow extends from Wire 1 to the mobile wire, labeled r. No other labels, lines, text, or axes appear.
Cross-sectional view of the parallel current-carrying wires.
Two long, straight, parallel wires, Wire 1 and Wire 2, are fixed in place separated by a distance \(d\) and carry equal currents \(I\) in the same direction. A third long wire, parallel to the first two and carrying the same current \(I\) in the same direction, is placed in the plane between them. In Scenario 1, the third wire is held at a distance of \(\dfrac{d}{3}\) from Wire 1, experiencing a net magnetic force of magnitude \(F_1\), and in Scenario 2, it is held at a distance of \(\dfrac{d}{5}\) from Wire 1, experiencing a net magnetic force of magnitude \(F_2\). What is the ratio \(\dfrac{F_2}{F_1}\)?

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