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AP Physics C: E&M
8.6 Gauss’s Law
IntermediateMCQMathematicalProportional Analysis22.6k
Two side-by-side circular diagrams. On the left, labeled Initial, a light-gray shaded circle of radius 2.0 cm is centered on a point. A horizontal solid arrow extends from the center to the right edge of the circle and is labeled \(R_0\). A filled black dot labeled \(P\) lies on the right edge of the circle at distance \(R_0\) from the center. The label \(Q\) is positioned above the circle. On the right, labeled Final, a larger concentric light-gray shaded circle of radius 4.0 cm is centered on a point. A horizontal solid arrow extends from the center to the right edge and is labeled \(2R_0\). A filled black dot labeled \(P\) is located at distance \(R_0\) from the center, positioned inside the shaded circle halfway along the radius. A thin dashed vertical reference line aligns point \(P\) between the two diagrams. No other labels, lines, text, or axes appear.
Uniformly charged insulating sphere before and after expanding from radius \(R_0\) to \(2R_0\).
A solid insulating sphere of radius \(R_0\) contains a total charge \(Q\) distributed uniformly throughout its volume. The sphere then expands uniformly to a new radius of \(2R_0\) while the total charge \(Q\) remains unchanged and uniformly distributed. What is the ratio of the magnitude of the electric field at a distance \(r = R_0\) from the center before the expansion to the magnitude of the electric field at that same distance after the expansion, \(\dfrac{E_{\text{initial}}}{E_{\text{final}}}\)?

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