Dielectrics and Polarisation - UNSOLVED PRACTICE SET

Q7. Distinguish between polar and non-polar dielectrics with one example of each.

Q8. What happens to the molecules of a non-polar dielectric when placed in an external electric field? Explain the process of induced polarization.

Q9. Why does the presence of a dielectric reduce the electric field between the plates of a capacitor? Explain in terms of polarization.

Q10. Water has a very high dielectric constant (≈ 80). Why is this property important in biological systems and chemical reactions?

Q11. Define dielectric strength. What happens when the electric field applied to a dielectric exceeds its dielectric strength?

Q12. A dielectric slab of dielectric constant K = 4 is inserted between the plates of a parallel plate capacitor. By what factor does the capacitance change if the battery remains connected?

Q13. Explain the phenomenon of polarization in dielectrics. Distinguish between polar and non-polar dielectrics with suitable examples and diagrams showing molecular behavior with and without an external electric field.

Q14. Derive the expression for the electric field inside a dielectric slab placed in a uniform external electric field E₀. Show that the net field inside the dielectric is E = E₀/K, where K is the dielectric constant.

Q15. A parallel plate capacitor has plate area A = 100 cm² and plate separation d = 2 mm. It is charged to a potential difference V = 100 V and then disconnected from the battery.

(a) Calculate the initial capacitance, charge, and energy stored.

(b) A dielectric slab of thickness 2 mm and dielectric constant K = 5 is inserted between the plates. Calculate the new capacitance, charge, and energy stored.

(c) Explain why the energy decreases when the dielectric is inserted.

[Given: ε₀ = 8.85 × 10⁻¹² C² N⁻¹ m⁻²]

Q16. A parallel plate capacitor has plates of area 200 cm² separated by 1 mm in air. It is connected to a 50 V battery.

(a) Calculate the capacitance, charge, and energy stored.

(b) A mica sheet of dielectric constant K = 6 and thickness 1 mm is inserted between the plates while the battery remains connected. Calculate the new capacitance, charge, and energy.

(c) Now the battery is disconnected and the mica sheet is removed. What are the new values of charge, potential difference, and energy?

(d) Compare the energy in parts (b) and (c) and explain the difference.

[Given: ε₀ = 8.85 × 10⁻¹² C² N⁻¹ m⁻²]

Q17. In a school science fair, a student demonstrates polarization using a plastic comb and small pieces of paper.

(a) Explain why the plastic comb, when rubbed through dry hair, attracts small pieces of paper. Is the comb a conductor or a dielectric?

(b) When the comb is brought near a stream of water from a tap, the water bends towards the comb. Explain this phenomenon in terms of polarization of water molecules.

(c) Would the same effect be observed if the comb were made of metal instead of plastic? Explain why or why not.

(d) Calculate the induced dipole moment in a water molecule if the electric field due to the comb at the molecule's position is 10⁴ N/C. [Given: polarizability of water ≈ 1.5 × 10⁻⁴⁰ C m²/V]

Q18. A dielectric slab of thickness t and dielectric constant K is inserted between the plates of a parallel plate capacitor of plate separation d (where t < d). The capacitor is connected to a battery of emf V.

(a) Derive the expression for the capacitance of this capacitor with the partially filled dielectric.

(b) Calculate the capacitance if A = 50 cm², d = 3 mm, t = 2 mm, K = 4, and V = 100 V.

(c) Find the electric field in the air gap and in the dielectric.

(d) Calculate the bound surface charge density on the dielectric surfaces.

[Given: ε₀ = 8.85 × 10⁻¹² C² N⁻¹ m⁻²]