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AP Physics C: E&M
13.2 Electromagnetic Induction
13.1 Magnetic Flux
AdvancedMCQMathematicalConceptual20.4k
A circular cross section of a solenoid with radius R centered at the origin, drawn with a solid circle. The interior of the circle contains a uniform pattern of exactly six dots indicating magnetic field directed perpendicular out of the page. A horizontal dashed reference line extends from the center origin to the right. Along this dashed line, point P_1 is marked with a solid dot at distance R/2 from the center, and point P_2 is marked with a solid dot at distance 2R from the center. Two concentric dashed circles centered at the origin pass through P_1 and P_2, representing circular paths of radius R/2 and 2R, respectively. A single radial dimension arrow extends from the center to the edge of the solid circle, labeled R. No other labels, lines, text, or axes appear.
Cross section of the solenoid showing points \(P_1\) and \(P_2\).
A long, ideal cylindrical solenoid of radius \(R\) has \(n\) turns per unit length and carries a time-dependent current \(I(t)\) that decreases at a constant rate \(\left|\dfrac{dI}{dt}\right| = C\). Points \(P_1\) and \(P_2\) lie in a plane perpendicular to the solenoid's central axis at radial distances \(r_1 = \dfrac{R}{2}\) and \(r_2 = 2R\) from the center, respectively. Which of the following correctly compares the magnitudes of the induced electric fields \(E_1\) at \(P_1\) and \(E_2\) at \(P_2\), and provides the correct physical justification?

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