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AP Physics C: E&M
10.1 Electrostatics with Conductors
8.6 Gauss’s Law
Multi-Unit
AdvancedMCQMathematicalConceptual16.3k
A cross-sectional view in the xy-plane showing a spherical conducting shell centered at origin O. A horizontal dashed line represents the x-axis and a vertical dashed line represents the y-axis, intersecting at O. An inner circle of radius a and an outer concentric circle of radius b are both centered at O, with the region between them filled with light gray shading to represent the conducting material. On the positive x-axis inside the cavity at distance d from O, a solid black dot is labeled +q. On the positive y-axis within the shaded region at radius (a+b)/2, a solid black dot is labeled P_{\text{cond}}. On the positive x-axis outside the shell at distance 2b from O, a solid black dot is labeled P_1. On the negative x-axis outside the shell at distance 2b from O, a solid black dot is labeled P_2. No other labels, lines, text, or axes appear.
Cross section of the charged conducting spherical shell with an eccentric point charge.
A thick, spherical conducting shell centered at the origin \(O\) has inner radius \(a\) and outer radius \(b\) and carries a net charge \(+Q\). Inside the cavity, a point charge \(+q\) is held fixed at position \((d, 0, 0)\), where \(0 < d < a\), and the entire system is in electrostatic equilibrium. Point \(P_{\text{cond}}\) is located within the conducting material at \((0, \frac{a+b}{2}, 0)\), point \(P_1\) is located outside the shell at \((2b, 0, 0)\), and point \(P_2\) is located outside the shell at \((-2b, 0, 0)\). Which of the following correctly compares the electric field magnitudes at these three points and characterizes the equipotential boundaries of the system?

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