A highly sensitive instrument detects nanoscale gaps by using an LC circuit with a parallel-plate capacitor having plate area A and known inductance L. The charge oscillates at a frequency f when the capacitor plates are separated by a distance x. The relationship between 𝑥, 𝜖₀, 𝐴, 𝑓, and 𝐿 is given by: x=4π2 Aϵ₀f²L.

If 𝑓 is on the order of 500 kHz and can be measured to a precision of Δ𝑓=0.5 Hz, with what percent accuracy can 𝑥 be determined? Fringing effects at the capacitor’s edges are ignored.