Question

A parallel plate capacitor is made of two circular plates separated by a distance of $5mm$ 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

Answer: 6

When free space between parallel plates of capacitor
$E=\frac{\sigma }{{ϵ}_0}$
When dielectric is introduced between parallel plates of capacitor $E^{\prime }=\frac{\sigma }{K{ϵ}_0}$
Electric field inside dielectric
$\frac{\sigma }{K{ϵ}_0}=3\times 10^4$
where, $K=$ dielectric constant of medium $=2.2$
${ϵ}_0=$ permit avity of free space $=8.85\times 10^{-12}$
$\Rightarrow \sigma =22\times 8.85\times 10^{-12}\times 3\times 10^4$
$=6\times 10^{-7}C/m^2$