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AP Physics C: E&M
12.4 Ampère’s Law
12.3 Magnetic Fields of Current-Carrying Wires and the Biot-Savart Law
AdvancedMCQMathematical22.5k
Cross section of the cylindrical conductor.
Cross section of the cylindrical conductor.
A long, solid cylindrical conductor of radius \(R\) carries a non-uniform current directed along its central axis. The current density inside the conductor varies with radial distance \(r\) from the axis according to \(J(r) = J_0 \left(1 - \dfrac{r}{R}\right)\) for \(r \le R\), where \(J_0\) is a positive constant. Which of the following expressions gives the magnitude of the magnetic field \(B(r)\) inside the conductor at a distance \(r < R\) from the central axis?

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