Q45 / 54 · JEE Advanced 2022 (Paper 1) · Physics

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 d2 from their original positions, as shown in Figure (b).

Figure

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?

  • A
    The electric field inside the dielectric material is reduced by a factor of 2 K.
  • Correct answer
    B
    The capacitance is decreased by a factor of 1K+1.
  • C
    The voltage between the capacitor plates is increased by a factor of K+1.
  • D
    The work done in the process DOES NOT depend on the presence of the dielectric material.

Solution

Figure

Capacitance of both capacitors are Ca=Kε0Ad and Cb=ε0Ad+dK=ε0AKdK+1

Now, charge stored is qa=Kε0AdV and qb=ε0AKVdK+1.

Electric field between each parallel plate capacitor is Ea=qaKAε0=Kε0AVdKε0A=Vd and

Ebdielectric=EairK=qbKAε0=ε0AKVdK+1KAε0=VdK+1

So, from above relations, we can see that capacitance decrease by a factor of 1K+1.

Work done in the process W=Uf-Ui

=12Cf-CiV2

=12ε0AKdK+1-Kε0AdV2

=12V2ε0AKd1K+1-1

=12ε0AKV2d1-K-1K+1

=12ε0AV2d-K2K+1

Thus, the work done in the process depends upon the dielectric material.

Hence, the correct answer is option: 'B'.

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