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AP Physics C: E&M
12.3 Magnetic Fields of Current-Carrying Wires and the Biot-Savart Law
AdvancedMCQMathematical15.9k
A Cartesian coordinate plane with horizontal axis labeled x and vertical axis labeled y, intersecting at the origin labeled (0,0). A closed planar loop lies entirely in the upper half-plane. The bottom boundary of the loop is an upward-opening parabolic curve labeled y = d + kx^2, with its vertex on the y-axis at (0,d). The top boundary of the loop is a horizontal straight line segment at height H, labeled y = H. The parabola and horizontal line intersect at two points, one at negative x and one at positive x. Two counterclockwise current arrows are shown on the perimeter of the loop: one arrow on the horizontal segment pointing to the left, and one arrow on the parabolic segment near its vertex pointing to the right, labeled I. A small dot marks the origin (0,0). No other labels, lines, text, or axes appear.
Planar conducting loop in the xy-plane carrying counterclockwise current I.
A planar conducting loop lies in the \(xy\)-plane and carries a steady counterclockwise current \(I\). The bottom portion of the loop is formed by the parabolic curve \(y = d + kx^2\), and the top is closed by the horizontal line segment \(y = H\), where \(d\), \(k\), and \(H\) are positive constants such that \(H > d\). Which of the following expressions correctly gives the \(z\)-component of the magnetic field, \(B_z\), at the origin \((0,0)\) due only to the parabolic segment of the loop?

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