# Find the potential difference across the plates given plate area, charge, and distance between plates? Why is k excluded from equation?

## Area= $0.2 {m}^{2}$ Distance=$1 m m$ Charge (both plates)=$4E-6 C$ ε_0=8.85E-12 $k = 9E9$ A) 0 B) $4E-2$ C) $1E2$ D)$2E2$ E)4$E 8$ The answer is D). I was more confused with how to get the right answer. I attempted to derive two equations to get V: C_(par.plates)=(kε_0A)/d and $V = \frac{Q}{C}$ to V=(Qd)/(kε_0A) But when I tried to solve for V it was incorrect. An internet search told me my equation was mostly correct, except k wasn't part of the equation. Why is this?

Here $k$ is not the Coulomb constant, which is the number you use. Rather, it is the relative permittivity of the dielectric. If it is air, $k = 1.00058986 \pm 0.00000050$ :)
Think $C = \frac{\textcolor{red}{{\epsilon}_{r}} {\epsilon}_{o} A}{d} \text{ with } {\epsilon}_{r} = 1$