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AP Physics C: E&M
10.2 Redistribution of Charge between Conductors
10.1 Electrostatics with Conductors
IntermediateMCQMathematicalProportional Analysis22k
Two circular outlines representing conducting spheres are positioned horizontally on a white background, separated by open space. The left circle, representing Sphere 1, has a smaller radius with a horizontal line segment from its center to its perimeter labeled \(R\), and the text label \(+Q\) positioned directly above the sphere. The right circle, representing Sphere 2, is three times the diameter of the first circle, with a horizontal line segment from its center to its perimeter labeled \(3R\), and the text label \(+5Q\) positioned directly above the sphere. A horizontal dimension line between the bottom centers of the two spheres is labeled \(d \gg R\). No other labels, lines, text, or axes appear.
Two conducting spheres of radii \(R\) and \(3R\) with initial charges \(+Q\) and \(+5Q\).
Two spherical conductors, Sphere 1 of radius \(R\) and Sphere 2 of radius \(3R\), are separated by a distance much greater than their radii. Initially, Sphere 1 carries a net charge of \(+Q\) and Sphere 2 carries a net charge of \(+5Q\). The spheres are momentarily connected by a thin conducting wire and then disconnected. What is the ratio of the final charge on Sphere 1 to its initial charge, \(\dfrac{q_{1,\text{final}}}{q_{1,\text{initial}}}\)?

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