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AP Physics C: E&M
8.4 Electric Fields of Charge Distributions
AdvancedMCQMathematical21.9k
A horizontal axis line labeled x with an arrow at the right end. A thick horizontal line segment representing a rod lies on the axis from a vertical tick mark at the origin labeled 0 to a vertical tick mark labeled L. Above the rod, a text label indicates \lambda(x) = \alpha x. To the right of the rod on the axis, a solid dot at a vertical tick mark labeled L + d represents point P. A horizontal dimension line with arrows at both ends extends below the axis from the tick mark at L to the tick mark at L + d and is labeled d. No other labels, lines, text, or axes appear.
Non-uniform charged rod along the x-axis with point P at distance d.
A thin, nonconducting rod of length L lies along the positive x-axis with its ends at x = 0 and x = L. The rod carries a non-uniform linear charge density given by \lambda(x) = \alpha x, where \alpha is a positive constant. Point P is located on the x-axis at x = L + d, a distance d from the right end of the rod. Which of the following integral expressions correctly gives the magnitude of the electric field at point P in terms of the given quantities and physical constants?

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