Question #42007

A point charge $+Q$ is fixed at the origin of a coordinate system. A small planar sensor of area $A$ is constrained to move along the curve $y = x^3$ (where $x > 0$) in the $xy$-plane. The sensor's surface normal $\hat{n}$ is mechanically maintained parallel to the positive $y$-axis ($\hat{n} = \hat{j}$). The magnitude of the electric field $E$ at the sensor's location is determined experimentally by measuring the electric flux $\Delta \Phi$ through the sensor, its area $A$, and its $x$-coordinate. During an experiment at $x = 1 \text{ m}$, the relative error in measuring the flux is $1.5\%$, and the relative error in measuring the area is $1.0\%$. The absolute error in measuring the $x$-coordinate is $0.02 \text{ m}$. Assuming the errors are independent and add up to give the maximum possible error, what is the maximum percentage relative error in the calculated value of the electric field $E$?