Question

when a potential difference of 150 V is applied to the plates of a parallel plate capacitor the plates carry a surface charge density of 30.0 nC/cm^2. what is the spacing between the plates?

Answer 1

The electric field between plates

$$E=\frac{\sigma}{\epsilon_0}=\frac{V}{d}.$$

Hence, the spacing between the plates

$$d=\frac{V\epsilon_0}{\sigma}=\frac{150\:\rm V\times 8.85\times 10^{-12}\:\rm F/m}{30.0\times 10^{5}\:\rm C/m^2}$$ $$=4.4\times 10^{-6}\:\rm m=4.4\:\rm \mu m$$