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AP Physics C: E&M
8.6 Gauss’s Law
AdvancedMCQMathematicalConceptual17.4k
A quantitative Cartesian plot of radial electric field \(E_r\text{ (kN/C)}\) on the vertical axis versus radial distance \(r\text{ (m)}\) on the horizontal axis. Light gray gridlines appear every \(0.05\text{ m}\) horizontally and every \(1\text{ kN/C}\) vertically. The horizontal axis is labeled \(r\text{ (m)}\) with labeled tick marks at 0, 0.10, 0.20, 0.30, and 0.40. The vertical axis is labeled \(E_r\text{ (kN/C)}\) with labeled tick marks at -6, -4, -2, 0, 2, 4, 6, 8, and 10. From \(r = 0\) to \(r = 0.10\text{ m}\), a solid curve starts at (0, 0) and curves upward smoothly to a peak at (0.10, 9). From \(r = 0.10\text{ m}\) to \(r = 0.20\text{ m}\), a solid curve decreases concave-upward from (0.10, 9) down to an open circle at (0.20, 2.25). A solid dot is placed at (0.20, 0). From \(r = 0.20\text{ m}\) to \(r = 0.30\text{ m}\), a heavy solid horizontal line lies directly along the axis at \(E_r = 0\), ending in an open circle at (0.30, 0). A solid dot is placed at (0.30, -5). From \(r = 0.30\text{ m}\) to \(r = 0.40\text{ m}\), a solid curve starts at (0.30, -5) and rises concave-downward toward zero. No other labels, lines, text, or axes appear.
Radial electric field \(E_r\) as a function of radial distance \(r\).
A system of concentric spherical objects centered at the origin produces the radial electric field component \(E_r\) shown in the graph as a function of radial distance \(r\). The system consists of an inner insulating sphere of radius \(r = 0.10\text{ m}\) and a concentric spherical conducting shell of inner radius \(r = 0.20\text{ m}\) and outer radius \(r = 0.30\text{ m}\). What is the net electric charge of the spherical conducting shell?

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