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AP Physics C: E&M
8.6 Gauss’s Law
8.5 Electric Flux
AdvancedMCQMathematicalConceptual16.6k
A three-dimensional Cartesian coordinate system shown in grayscale with three mutually perpendicular axes labeled \(x\), \(y\), and \(z\). The vertical axis is labeled \(z\) at its top arrow. The \(x\)-axis extends forward and to the left, and the \(y\)-axis extends to the right. A flat square plate lies entirely in the \(xy\)-plane, centered at the origin, with its edges parallel to the \(x\)- and \(y\)-axes. Tick marks on the \(x\)-axis are labeled \(-L\) and \(L\), and tick marks on the \(y\)-axis are labeled \(-L\) and \(L\). A filled black circle representing a point charge sits on the positive \(z\)-axis at a height labeled \(d\), with the text label \(+q\) adjacent to it. A straight dashed line segment connects the point charge to an arbitrary point \((x, y, 0)\) on the square plate. No other labels, lines, text, or axes appear.
A point charge \(+q\) on the \(z\)-axis above a square plate centered at the origin in the \(xy\)-plane.
A point charge \(+q\) is fixed on the \(z\)-axis at the coordinates \((0, 0, d)\), where \(d > 0\). A flat, nonconducting square plate with side length \(2L\) lies in the \(xy\)-plane and is centered at the origin, spanning the region \(-L \le x \le L\) and \(-L \le y \le L\). Which of the following expressions represents the magnitude of the electric flux passing through the plate?

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