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AP Physics C: E&M
8.3 Electric Fields
8.1 Electric Charge and Electric Force
AdvancedMCQMathematicalProportional Analysis25.4k
A Cartesian coordinate system with a horizontal x-axis and a vertical y-axis intersecting at an origin labeled O. On the positive y-axis, a solid black circle represents a charge labeled +q located at a distance a above the origin, indicated by a vertical dimension line labeled a. On the negative y-axis, an open circle with a black border represents a charge labeled -q located at a distance a below the origin, indicated by a vertical dimension line labeled a. On the positive x-axis, a black dot marks a point labeled P located at a distance x to the right of the origin, indicated by a horizontal dimension line along the axis labeled x. Straight dashed lines connect the charge +q to point P and the charge -q to point P. No other labels, lines, text, or axes appear.
Two point charges, +q and -q, on the y-axis with point P on the x-axis.
Two point charges, \(+q\) and \(-q\), are held fixed on the \(y\)-axis at \((0, a)\) and \((0, -a)\), respectively, in vacuum.

Point \(P\) is located on the positive \(x\)-axis at a distance \(x\) from the origin.

Which of the following correctly gives the net electric field vector \(\vec{E}(x)\) at point \(P\) and the power-law exponent \(n\) describing the asymptotic dependence of its magnitude, \(E(x) \propto x^n\), in the limit \(x \gg a\)?

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