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AP Physics C: E&M
12.4 Ampère’s Law
IntermediateMCQMathematicalProportional Analysis25k
A circular cross section of a cylindrical conductor of radius \(R\), centered at a point marked with a small central dot. A shaded circular region represents the conductor cross section. A horizontal dashed reference line extends to the right from the center. Along this line, two small filled circular points are marked: Point 1 at a distance of \(R/4\) from the center, and Point 2 at a distance of \(2R\) from the center, outside the shaded circle. A double-headed arrow labeled \(R\) extends from the center to the outer perimeter of the shaded circle at an angle of 45 degrees above the horizontal. Current direction is indicated by an encircled dot symbol labeled \(I_0\) placed in the upper-left quadrant of the shaded region. Point 1 has the label \(P_1\) directly above it, and Point 2 has the label \(P_2\) directly above it. No other labels, lines, text, or axes appear.
Cross-sectional view of the current-carrying wire and observation points.
A long, straight, solid cylindrical wire of radius \(R\) carries a steady current \(I_0\) that is uniformly distributed over its cross-sectional area. Point 1 is located inside the wire at a radial distance \(r_1 = \dfrac{R}{4}\) from the central axis, and Point 2 is located outside the wire at a radial distance \(r_2 = 2R\) from the central axis. What is the ratio \(\dfrac{B_2}{B_1}\) of the magnetic field magnitude at Point 2 to the magnetic field magnitude at Point 1?

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