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

Answer 1

Answer: (A), (D)

As $E=V / d$
$E _{1} / E _{2}=1$ (both parts have common potential difference)
Assume $C _{0}$ be the capacitance without dielectric for whole capacitor.
$k \frac{ C _{0}}{3}+\frac{2 C _{0}}{3}= C$
$\frac{ C }{ C _{1}}=\frac{2+ k }{ k }$
$\frac{ Q _{1}}{ Q _{2}}=\frac{ k }{2}$