JEE Advanced 2022 · Paper 1 · Physics Q9

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PhysicsMultiple correct+4 / -2Question 27 of 54

A medium having dielectric constant $K > 1$ fills the space between the plates of a parallel plate capacitor. The plates have large area, and the distance between them is $d$ . The capacitor is connected to a battery of voltage $V$ , as shown in Figure (a). Now, both the plates are moved by a distance of $\dfrac d2$ from their original positions, as shown in Figure (b).

In the process of going from the configuration depicted in Figure (a) to that in Figure (b), which of the following statement(s) is(are) correct?

Figure (a): a parallel-plate capacitor with plate separation d completely filled by a dielectric slab of thickness d, connected to a battery V. Figure (b): the same slab and battery, with each plate moved outward by d/2, leaving an air gap of d/2 on each side of the slab (total separation 2d).

The electric field inside the dielectric material is reduced by a factor of

2K

The capacitance is decreased by a factor of

\dfrac{1}{K+1}

The voltage between the capacitor plates is increased by a factor of

(K+1)

The work done in the process DOES NOT depend on the presence of the dielectric material.

Answer and worked solution

Official answer: B

Capacitances. The battery keeps the voltage at $V$ throughout. With the slab of thickness $d$ and air gaps totalling $d$ :
$C_a=\frac{K\epsilon_0A}{d},\qquad C_b=\frac{\epsilon_0A}{d/K+d}=\frac{K\epsilon_0A}{d(K+1)}.$
So $C$ is reduced by the factor $\frac1{K+1}$ . (B) true.

(A) False. The field in the dielectric goes from $\frac Vd$ to $\frac{V}{d(K+1)}$ , i.e. it falls by the factor $K+1$ , not $2K$ .

(C) False. The voltage stays $V$ .

(D) False. The work done depends on $K$ , through the charge change $\Delta Q=V\Delta C$ .

Topics:Dielectrics Energy stored in a capacitor

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JEE Advanced 2022 · Paper 1, Physics question 9