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)

The correct options are
A $\frac{E_1}{E_2}=1$
D $\frac{C}{C_1}=\frac{2+K}{K}$

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.
$K\frac{C_0}{3}+\frac{2C_0}{3}=C$
$\frac{C}{C_1}=\frac{2+K}{K}$
$\frac{Q_1}{Q_2}=\frac{K}{2}$