An advanced sensor is used to detect gaps in the nanoscale using inductance. Consider forming an LC circuit using a parallel-plate capacitor with plate area 𝐴 and a known inductance 𝐿. If the charge is found to oscillate in this circuit at a frequency 𝑓=𝜔/2𝜋 when the capacitor plates are separated by distance 𝑥, derive an expression for 𝑥 in terms of 𝜖₀, 𝐴, 𝑓, and 𝐿.