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AP Physics C: E&M
9.2 Electric Potential
9.1 Electric Potential Energy
8.6 Gauss’s Law
Multi-Unit
AdvancedMCQMathematicalConceptual22.4k
A cross-sectional diagram showing a central small filled circle labeled +Q at the center of a thin circular ring of radius R. A radial dashed line extends horizontally to the right from the center past the ring. On this dashed line, three positions are indicated: a point at r = R/2 labeled with a small open circle and +q_0, the intersection with the ring at r = R, and a point at r = 2R marked with a small dot. A single horizontal arrow points to the right from r = R/2 toward r = 2R. The ring is labeled with net charge -2Q near its top edge. A radial arrow points from the center toward the upper-right at 45 degrees to the ring with label R. No other labels, lines, text, or axes appear.
A central point charge enclosed by a concentric thin spherical conducting shell.
A system consists of a stationary point charge \(+Q\) fixed at the origin and an isolated, thin spherical conducting shell of radius \(R\) concentric with the point charge. The shell carries a net charge of \(-2Q\), and a tiny aperture in the shell allows particles to pass through without making electrical contact. A test particle of charge \(+q_0\) is moved radially outward from \(r = \dfrac{R}{2}\) to \(r = 2R\). What is the work done by the electric field of the system on the test particle during this displacement?

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