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AP Physics C: E&M
12.4 Ampère’s Law
AdvancedMCQMathematical22.2k
Cross section of the cylindrical conductor and circular Amperian loop of radius \(r\).
Cross section of the cylindrical conductor and circular Amperian loop of radius \(r\).
A long, solid cylindrical wire of radius \(R\) carries current directed parallel to its central axis. The current density within the wire is non-uniform and depends on the radial distance \(r\) from the central axis according to \(J(r) = C r^2\), where \(C\) is a positive constant. Which of the following integral expressions represents a correct setup using Ampère's law to determine the magnitude of the magnetic field \(B(r)\) at a distance \(r < R\) from the central axis?

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