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title: "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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url: "https://nerd-notes.com/ubq/124742/"
date_modified: "2026-09-28T14:09:41+00:00"
---

# 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?

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?

![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.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604580-A2VU6E.jpg)

- **A.** \(E_1 > E_2 > E_{\text{cond}} = 0\); the equipotential surfaces in the region \(r > b\) are spheres centered at \((d, 0, 0)\), and the inner surface \(r = a\) is at a higher electric potential than the outer surface \(r = b\).
- **B.** \(E_1 > E_2 > E_{\text{cond}} = 0\); the equipotential surfaces in the region \(r > b\) are spheres centered at the origin \((0, 0, 0)\), and the inner surface \(r = a\) is at the same electric potential as the outer surface \(r = b\).
- **C.** \(E_1 = E_2 > E_{\text{cond}} > 0\); the equipotential surfaces in the region \(r > b\) are non-spherical surfaces elongated along the \(x\)-axis, and the inner surface \(r = a\) is at the same electric potential as the outer surface \(r = b\).
- **D.** \(E_1 = E_2 > E_{\text{cond}} = 0\); the equipotential surfaces in the region \(r > b\) are spheres centered at the origin \((0, 0, 0)\), and the inner surface \(r = a\) is at the same electric potential as the outer surface \(r = b\).

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124742/*