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AP Physics C: E&M
9.2 Electric Potential
IntermediateMCQMathematical21.7k
A Cartesian coordinate system in the xy-plane showing a horizontal x-axis and a vertical y-axis intersecting at the origin labeled O. A solid, curved semicircle of radius R lies entirely in the right half-plane, extending continuously from the point (0, -R) on the negative y-axis through (R, 0) on the positive x-axis to (0, R) on the positive y-axis. A thin dashed straight line connects the origin to a generic point on the semicircle in the first quadrant, with a single straight arrow along this dashed line labeled R pointing toward the upper-right at 45 degrees. A small curved angle arc labeled \theta extends counterclockwise from the positive x-axis to the dashed line. Near the apex of the semicircle, the label \lambda(\theta) = \lambda_0 \cos\theta appears. No other labels, lines, text, or axes appear.
Semicircular charged arc of radius \(R\) centered at the origin in the \(xy\)-plane.
A thin, nonconducting semicircular arc of radius \(R\) is fixed in the \(xy\)-plane and centered at the origin. The arc extends from \(\theta = -\dfrac{\pi}{2}\) to \(\theta = \dfrac{\pi}{2}\), where \(\theta\) is measured counterclockwise from the positive \(x\)-axis. The linear charge density along the arc varies according to \(\lambda(\theta) = \lambda_0 \cos\theta\), where \(\lambda_0\) is a positive constant. Assuming the electric potential is zero at infinity, which of the following expressions correctly represents the integral setup to determine the electric potential \(V\) at the origin?

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