Question

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=`1mm`
Charge (both plates)=`4E-6C`
`ε_0=8.85E-12`
`k=9E9`

A) 0
B) `4E-2`
C) `1E2`
D)`2E2`
E)4`E8`

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=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?

Answer 1

You've got your constants mixed up.

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 = (color(red)(epsilon_r) epsilon_o A)/(d) " with " epsilon_r = 1`