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AP Physics C: E&M
8.6 Gauss’s Law
8.5 Electric Flux
AdvancedMCQMathematicalConceptual19.6k
A three-dimensional Cartesian coordinate system showing axes labeled x, y, and z. In the xy-plane, a square with side length L lies with one vertex at the origin (0,0,0) and opposite diagonal vertex at (L,L,0), shaded light gray. A vertical dashed line extends along the z-axis from the origin to a height L, terminating at a solid black dot labeled Position 1 at (0,0,L). A second vertical dashed line rises from the geometric center of the gray square at (L/2, L/2, 0) to a height of L/2, terminating at a second solid black dot labeled Position 2 at (L/2, L/2, L/2). Thin dashed lines outline a cube of edge length L resting on the square surface to indicate perspective. No other labels, lines, text, or axes appear.
Square surface in the xy-plane and charge positions for Scenarios 1 and 2.
A flat, square surface of side length \(L\) lies in the \(xy\)-plane with vertices at \((0,0,0)\), \((L,0,0)\), \((L,L,0)\), and \((0,L,0)\). In Scenario 1, a point charge \(+q\) is fixed at position \((0,0,L)\), producing an electric flux of magnitude \(\Phi_1\) through the surface. In Scenario 2, the point charge \(+q\) is instead fixed at position \((L/2, L/2, L/2)\), producing an electric flux of magnitude \(\Phi_2\) through the surface. What is the ratio \(\Phi_2 / \Phi_1\)?

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