Q4. In steady state at constant field and physical conditions, assertion: the drift velocity of electrons in a wire does not grow with time, though every electron is accelerated by the field. Reason: each collision randomises an electron’s velocity, and on average an electron has been accelerating for only a time τ since its last collision. Are both true, and does the reason explain the assertion?
Both are true, and the reason explains the assertion (NCERT pages 85–86 and Example 3.2(b), page 88).
Q5. The potential difference across a metal wire is doubled, its temperature staying the same. What happens to the drift speed?
The field E = V/l doubles, and vd = eEτ/m with τ unchanged, so the drift speed doubles (NCERT Eq. (3.17), page 86).
Q6. Two wires of the same metal carry the same current, but one has twice the cross-section of the other. Compare their drift speeds.
I = neA|vd| with the same I, n and e, so vd ∝ 1/A: the thicker wire has half the drift speed (NCERT Eq. (3.18), page 86).
Q7. A copper wire 3.0 m long, of cross-section 2.0 × 10−6 m2, carries 3.0 A. With n = 8.5 × 1028 m−3, what is the mean drift-transport timescale l/v_d along the wire (NCERT Exercise 3.9)?
Here neA = 8.5 × 1028 × 1.6 × 10−19 × 2.0 × 10−6 = 2.72 × 104 C m−1, so vd = 3.0/(2.72 × 104) ≈ 1.1 × 10−4 m/s. This is a mean transport timescale, not the actual travel time of each randomly moving electron. The time is l/vd ≈ 2.72 × 104 s, about 7.6 hours (NCERT Eq. (3.18), page 86).