Question

A parallel plate capacitor of capacitance $200\text{pF}$ having area $100{\text{cm}}^2$ is completely filled with a dielectric material of dielectric constant $k=2.8$ at $20\text{V}$ potential difference, find the magnitude of electric field in the dielectric.

• A. $1.2\times {10}^4\text{V/m}$
• B. $1.5\times {10}^4\text{V/m}$
• C. $1.6\times {10}^6\text{V/m}$
• D. $1.6\times {10}^4\text{V/m}$

Answer 1

The correct option is D $1.6\times {10}^4\text{V/m}$

Given, $C=200\text{pF}$, $k=2.8$ and $V=20\text{V}$

As we know, electric field in the region between the plate is given by
$E=\frac{V}{d}.......\left(1\right)$
and capacitance of a capacitor with dielectric is given by $C=\frac{k{\epsilon }_{0}A}{d}$
$\Rightarrow d=\frac{k{\epsilon }_{0}A}{C}$

Substituting the value of $d$ in equation $\left(1\right)$ we get,

$E=\frac{VC}{k{\epsilon }_{0}A}=\frac{\left(20\right)(200\times {10}^{-12})}{2.8\times 8.85\times {10}^{-12}\times 100\times {10}^{-4}}$

$E=\frac{4000}{0.24}=1.6\times {10}^4\text{V/m}$

Why this question? To understand the effect of introduction of dielectric in a parallel plate capacitor.