A parallel-plate capacitor has plate…

A parallel-plate capacitor has plate area A and separation d; its capacitance with air between the plates is C0. A dielectric slab of constant K=3…

One or more options correct

A parallel-plate capacitor has plate area

A

and separation

d

; its capacitance with air between the plates is

C_0

. A dielectric slab of constant

K=3

, with the same area as the plates and thickness

d/2

, is placed flush against one plate, leaving an air gap of

d/2

. The capacitor is connected to a battery of emf

V

. Which of the following statements is/are correct?

A. The electric field in the air gap is $\dfrac{3V}{2d}$ .
B. The potential difference across the dielectric slab is $\dfrac{V}{4}$ .
C. The battery remains connected and the slab is slowly withdrawn completely; the external agent does work $\dfrac{C_0V^2}{4}$ .
D. If the battery is first disconnected and the slab then withdrawn slowly, the external agent again does work $\dfrac{C_0V^2}{4}$ .

Show answer and solution

Answer: A, B, C

The two layers are in series:

\dfrac1C=\dfrac{d/2}{\varepsilon_0A}+\dfrac{d/2}{3\varepsilon_0A}=\dfrac{2d}{3\varepsilon_0A}

, so

C=1.5C_0

and

Q=1.5C_0V

. Field in air

=\sigma/\varepsilon_0=\dfrac{Q}{\varepsilon_0A}=\dfrac{1.5V}{d}\cdot

using

C_0=\varepsilon_0A/d

, i.e.

\dfrac{3V}{2d}

: (A) correct. Field in dielectric is one third of this,

\dfrac{V}{2d}

, over

d/2

gives a drop of

V/4

: (B) correct. With battery connected,

U_i=\tfrac12(1.5C_0)V^2

U_f=\tfrac12C_0V^2

, battery work

=(C_0-1.5C_0)V^2=-0.5C_0V^2

(battery absorbs charge). Energy balance:

W_{ext}+W_{batt}=\Delta U

, so

W_{ext}=-0.25C_0V^2+0.5C_0V^2=\dfrac{C_0V^2}{4}

: (C) correct. With the battery disconnected,

Q

is fixed,

U_f=Q^2/2C_0=1.125C_0V^2

and

W_{ext}=1.125-0.75=\dfrac{3C_0V^2}{8}\neq\dfrac{C_0V^2}{4}

: (D) is false.

Original question written in the JEE Advanced 2025 Paper 2 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake