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AP Physics C: E&M
9.2 Electric Potential
BeginnerMCQMathematical19.6k
Two side-by-side scenarios labeled Scenario 1 and Scenario 2. On the left, Scenario 1 shows a shaded circle of radius R centered at the origin, labeled +Q. Dashed concentric circular paths of radii R and 2R encircle the center. A horizontal dashed line extends from the center outward to the right, with tick marks labeled r = R and r = 2R. On the right, Scenario 2 shows a small solid dot representing a point charge, labeled +Q. Dashed concentric circular paths of radii R and 2R surround the point charge, with a horizontal dashed line extending to the right with tick marks labeled r = R and r = 2R. No other labels, lines, text, or axes appear.
Comparison of a uniformly charged sphere and a point charge.
A solid insulating sphere of radius \(R\) carries a net charge \(+Q\) distributed uniformly throughout its volume. A separate point charge \(+Q\) is isolated in space. Let \(\Delta V_{\text{sphere}}\) be the magnitude of the electric potential difference between radial distances \(r = R\) and \(r = 2R\) from the center of the sphere, and let \(\Delta V_{\text{point}}\) be the magnitude of the electric potential difference between distances \(r = R\) and \(r = 2R\) from the point charge. What is the ratio \(\dfrac{\Delta V_{\text{sphere}}}{\Delta V_{\text{point}}}\)?

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