Q4. Assertion: winding more turns on a coil increases the emf induced in it by a given change of field. Reason: each turn has the same rate of change of flux, and the emfs of the turns add. Are both true, and does the reason explain the assertion?
Both are true, and the reason explains the assertion: ε = −N dΦB/dt, so the emf grows in proportion to N (NCERT Eq. (6.4), page 158).
Q5. A 200-turn coil of area 4.0 × 10−3 m2 and resistance 8.0 Ω lies with its plane perpendicular to a field that falls steadily from 0.50 T to 0.10 T in 0.020 s. Neglect self-inductance and find the magnitudes of the average emf, current and transferred charge.
ΔΦB = 0.40 × 4.0 × 10−3 = 1.6 × 10−3 Wb per turn, so ε = 200 × 1.6 × 10−3/0.020 = 16 V and I = 16/8.0 = 2.0 A (NCERT Eq. (6.4), page 158). The charge is IΔt = 2.0 × 0.020 = 0.040 C. Since IΔt = NΔΦB/R, the charge does not depend on how quickly the field changes (reasoned).
Q6. Which of these doubles the average emf induced in a coil: (a) doubling the number of turns, (b) doubling the area of each turn, the uniform field change and orientation being the same, (c) taking twice as long over the same change of flux?
(a) and (b) double it, since ε = NΔΦB/Δt and ΔΦB is proportional to the area. (c) halves it (NCERT Eqs. (6.1) and (6.4), pages 157–158).
Q7. The flux through each turn of a 100-turn coil is ΦB = 2.0 × 10−3 sin(100πt) Wb. Find the largest emf induced in the coil.
ε = −N dΦB/dt = −100 × 2.0 × 10−3 × 100π cos(100πt), whose largest size is 100 × 2.0 × 10−3 × 100π ≈ 63 V (NCERT Eq. (6.4), page 158). The emf is largest when the flux is zero, and zero when the flux is largest (reasoned).