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AP Physics C: E&M
12.3 Magnetic Fields of Current-Carrying Wires and the Biot-Savart Law
AdvancedMCQMathematicalConceptual16.9k
A Cartesian coordinate plane with horizontal axis labeled x and vertical axis labeled y, intersecting at origin O. A thick solid line represents a wire carrying current I. The wire begins on the negative x-axis with an open end at the far left, extends along the horizontal axis to point (-R, 0), curves smoothly upward as a quarter-circle arc of radius R centered at O through the second quadrant to point (0, R) on the positive y-axis, and continues vertically upward along the positive y-axis with an open end at the top. Three small arrowheads along the wire indicate current direction: one pointing rightward along the negative x-axis, one pointing along the curved arc toward the positive y-axis, and one pointing upward along the positive y-axis. A label I is positioned adjacent to the wire. A radial dashed line segment connects origin O to the curved arc, labeled R. No other labels, lines, text, or axes appear.
A current-carrying wire consisting of two straight segments and a quarter-circular arc.
A thin wire carrying a steady current \(I\) lies in the \(xy\)-plane and consists of three connected sections: a semi-infinite straight section extending along the negative \(x\)-axis from \(x = -\infty\) to \(x = -R\), a quarter-circular arc of radius \(R\) centered at the origin connecting \((-R, 0)\) to \((0, R)\), and a semi-infinite straight section extending along the positive \(y\)-axis from \(y = R\) to \(y = +\infty\). Current \(I\) flows continuously through the sections in that order. Which of the following correctly describes the magnitude and direction of the net magnetic field \(\vec{B}\) at the origin?

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