Question

A parallel plate capacitor has a dielectric slab of dielectric constant K between its plates that covers 1/3 of the area of its plates, as shown in the figure. The total capacitance of the capacitor is C while that of the portion with dielectric in between is $C_1$. When the capacitor is charged, the plate area covered by the dielectric gets charge $Q_1$ and the rest of the area gets charge $Q_2$. The electric field in the dielectric is $E_1$ and that in the other portion is $E_2$. Choose the correct option/options, ignoring edge effects.

• A. $\frac{C}{C_1}=\frac{2+K}{K}$
• B. $\frac{E_1}{E_2}=\frac{1}{K}$
• C. $\frac{Q_1}{Q_2}=\frac{3}{K}$
• D. $\frac{E_1}{E_2}=1$

Answer 1

Answer: (A), (D)

$\frac{E_1}{E_2}=1$

$C=C_1+C_2$
$C_1=\frac{K{\epsilon }_{0}A/3}{d},C_2=\frac{{\epsilon }_{0}2A/3}{d}$
$\Rightarrow C=\frac{(K+2){\epsilon }_{0}A}{3d}$
$\Rightarrow \frac{C}{C_1}=\frac{K+2}{K}$
Also, $E_1=E_2=\frac{V}{d},$ where V is potential difference between the plates.