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.

Options

A. (a) `E_1/E_2=1`
B. (b) `E_1/E_2=1/K`
C. (c) `Q_1/Q_2=3/K`
D. (d) `C/C_1=(2+K)/(K)`

Answer

A, D

Explanation

This is a combination of two capacitors in parallel.
Therefore
`C=C_1+C_2` `:.` `C_2=C-C_1`
where `C_1=(kA)/(3 in_0d)` and `C-C_1=(2A)/(3 in_0d)`
`:.` (C-C_1)/(C_1)=2/k`
`:.` `C/C_1-1=2/k`
`:.` `C/C_1=2/k+1`
`C/C_1=2/k+1`
`:.` (d) is a correct option.
Now, `Q_1=C_1V=(kA)/(3in_0d)xxV`
and `Q_2=(C-C_1)V=(2A)/(3in_0d)xxV`
`:.` `Q_1/Q_2=k/2` `:.` (c) is incorrect
Aslo `V=Exxd`
`:.` `E=V/d=E_1=E_2` `:.` (a) is a correct option