Q4. Assertion: the field between the plates of a large parallel plate capacitor is uniform. Reason: between the plates the fields of the two oppositely charged sheets add, and each sheet’s field does not depend on the distance from it. Are both true, and does the reason explain the assertion?
Both are true, and the reason explains the assertion: each sheet gives σ/(2ε0) at every distance, so the sum σ/ε0 is the same everywhere between the plates, away from the edges (NCERT Chapter 1, page 35, and pages 68–69).
Q5. What plate area is needed for a 1.0 µF parallel plate capacitor with a vacuum gap of 0.10 mm?
A = Cd/ε0 = 1.0 × 10−6 × 1.0 × 10−4/(8.854 × 10−12) ≈ 11 m2 (NCERT Eq. (2.43), page 69).
Q6. A parallel plate capacitor has a field of 3.0 × 104 V/m between its plates, which are 4.0 mm apart. Find the potential difference and the surface charge density on the plates.
V = Ed = 3.0 × 104 × 4.0 × 10−3 = 120 V. σ = ε0E = 8.854 × 10−12 × 3.0 × 104 ≈ 2.7 × 10−7 C m−2 (NCERT Eqs. (2.41)–(2.42), page 69).