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Concepts Of Physics MCQ Edition [Volume 2]
Exam
Concepts Of Physics MCQ Edition [Volume 2]
Subject
Physics
Chapter
Capacitors

Concepts Of Physics MCQ Edition [Volume 2] · Physics · Capacitors

A dielectric slab is introduced between the plates of an isolated...

A dielectric slab is introduced between the plates of an isolated capacitor. The force acting between the plates will

Options

  1. Adecrease
  2. Bbecome zero
  3. Cremain unchanged
  4. Dincrease

Correct answer

C. remain unchanged

Step-by-step solution

For an isolated capacitor, the charge QQ on the plates remains constant.

The force between the plates of a capacitor can be calculated using the relation F=−dUdxF = -\dfrac{dU}{dx}, where UU is the electrostatic potential energy stored in the capacitor and xx is the separation between the plates.

When a dielectric slab of thickness tt and dielectric constant KK is introduced between the plates, the capacitance becomes:
C=ϵ0Ax−t+tKC = \dfrac{\epsilon_0 A}{x - t + \dfrac{t}{K}}

The energy stored in the capacitor is:
U = \dfrac{Q^2}{2C} = \dfrac{Q^2}{2\epsilon_0 A} \left( x - t +\dfrac{t}{K} \right)

Differentiating UU with respect to xx to find the force:
F=F =-\dfrac{dU}{dx} = -\dfrac{Q^2}{2\epsilon_0 A}

The magnitude of the force is ∣F∣=|F| =\dfrac{Q^2}{2\epsilon_0 A}, which is exactly the same as the force between the plates in the absence of the dielectric slab.

Alternatively, the electric field produced by one plate at the location of the other is E=E =\dfrac{Q}{2A\epsilon_0}. The polarized dielectric slab produces zero net electric field outside its volume. Thus, the field experienced by the charge on the other plate remains unaffected, and the force F=QEF = QE remains unchanged.
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