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
- Adecrease
- Bbecome zero
- Cremain unchanged
- Dincrease
Correct answer
C. remain unchanged
Step-by-step solution
For an isolated capacitor, the charge on the plates remains constant.
The force between the plates of a capacitor can be calculated using the relation , where is the electrostatic potential energy stored in the capacitor and is the separation between the plates.
When a dielectric slab of thickness and dielectric constant is introduced between the plates, the capacitance becomes:
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 with respect to to find the force:
-\dfrac{dU}{dx} = -\dfrac{Q^2}{2\epsilon_0 A}
The magnitude of the force is \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 \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 remains unchanged.
The force between the plates of a capacitor can be calculated using the relation , where is the electrostatic potential energy stored in the capacitor and is the separation between the plates.
When a dielectric slab of thickness and dielectric constant is introduced between the plates, the capacitance becomes:
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 with respect to to find the force:
-\dfrac{dU}{dx} = -\dfrac{Q^2}{2\epsilon_0 A}
The magnitude of the force is \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 \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 remains unchanged.