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AP Physics C: E&M
12.4 Ampère’s Law
IntermediateMCQMathematicalProportional AnalysisConceptual16.5k
A circular cross section of a long wire centered at the origin, with outer solid boundary of radius \(R\). A solid dot marks the central axis at the center. Shading across the interior of the circle represents a uniform current density \(J_0\) directed perpendicularly out of the page. A concentric dashed circle of radius \(r\) lies entirely inside the outer boundary, where \(r < R\). A straight solid arrow extends horizontally from the center to the right edge of the dashed circle, labeled \(r\) above the arrow. A second straight solid arrow extends from the center toward the upper-right at 45 degrees to the outer solid circle, labeled \(R\) along the arrow. No other labels, lines, text, or axes appear.
Cross section of the wire of radius \(R\) with an Amperian loop of radius \(r\).
An experiment is conducted to determine the uniform current density \(J_0\) inside a long, solid cylindrical conducting wire of radius \(R\). Miniature sensors measure the magnitude of the magnetic field \(B\) at various radial distances \(r\) from the central axis inside the wire (\(r < R\)). To produce a linear graph that can be used to determine \(J_0\), which quantities should be plotted on the vertical and horizontal axes, and what is the slope \(m\) of the resulting best-fit line?

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