Question

A parallel plate capacitor is made of two circular plates separated by a distance of $5\,mm$ and with a dielectric of dielectric constant $2.2$ between them. When the electric field in the dielectric is $3\times 10^{4}V/m,$ the charge density of the positive plate will be close to $......10^{- 7}C/m^{2}.$

Answer 1

When free space between parallel plates of capacitor
$E=\frac{\sigma }{\epsilon _{0}}$
When dielectric is introduced between parallel plates of capacitor $E'=\frac{\sigma }{K \epsilon _{0}}$
Electric field inside dielectric
$\frac{\sigma }{K \epsilon _{0}}=3\times 10^{4}$
where, $K=$ dielectric constant of medium $=2.2$
$\epsilon _{0}=$ permit avity of free space $=8.85\times 10^{- 12}$
$\Rightarrow \sigma =22\times 8.85\times 10^{- 12}\times 3\times 10^{4}$
$=6\times 10^{- 7}C/m^{2}$