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AP Physics C: E&M
12.3 Magnetic Fields of Current-Carrying Wires and the Biot-Savart Law
AdvancedMCQMathematicalConceptual14.5k
A schematic of two identical circular coils aligned coaxially along a horizontal central axis labeled z. The left coil of radius R is centered at z = -s/2, and the right coil of radius R is centered at z = +s/2, separated by horizontal distance s. The coils are rendered as vertically oriented ellipses to indicate three-dimensional perspective. On each coil, an arrow along the perimeter indicates current I circulating in the same direction. A horizontal dashed line represents the central axis passing through the centers of both coils, with a vertical tick mark at the midpoint labeled z = 0. A double-headed horizontal arrow below the coils indicates the separation labeled s. A vertical arrow extending from the center of the left coil to its upper edge is labeled R. No other labels, lines, text, or axes appear.
Two coaxial coils of radius R separated by distance s with currents in the same direction.
Two identical circular coils, each of radius \(R\), are placed coaxially along the \(z\)-axis with their centers at \(z = -s/2\) and \(z = +s/2\), where the origin \(z = 0\) is defined at the midpoint between them. The coils carry equal constant currents in the same direction, and their separation is set to \(s = R\) to create a region of near-uniform magnetic field centered at the origin. Which of the following statements correctly describes the behavior of the net axial magnetic field \(B(z)\) near \(z = 0\) and provides the correct physical and mathematical justification?

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