If you measure the size of each plate to be 12 cm2, how far apart are the plates, in micrometers?

Question

 A 0.054 μF capacitor is being held at a potential difference of 431 μV. I keep getting an answer 1.967 * 1o^-7 which is wrong. Please explain and show your work. Thanks!

Answer 1

I used the relation C = ε_o x A / d or d = ε_o x A / C.

d = 8.85 x 10^-12 F/m x 0.12² m²/ 0.054 x 10^-6 F = 2.36 x 10^-6 m or 2.34 μm.

Another approach is to use C = Q/V or Q = CV, then σ = Q/A, E = σ/ε_o = V/d , d = Vε_o / σ.