Q4. Assertion: diamagnetism is present in all substances. Reason: when a field is applied, the orbiting electrons of every atom develop an induced magnetic moment opposite to the field. Are both true, and does the reason explain the assertion?
Both are true, and the reason explains the assertion: the induced, opposing orbital moment arises in every atom, so diamagnetism is universal, though in paramagnetic and ferromagnetic substances it is masked (NCERT page 148; Points to Ponder 6, page 152).
Q5. NCERT gives χ ≈ −10−5 for a typical diamagnetic material and χ ≈ +10−5 for a typical paramagnetic one. Find μr for each, and by what fraction B differs from the vacuum value μH at the same internal H (neglect shape corrections).
μr = 1 + χ = 0.999 99 and 1.000 01. Since B = μrμH, the field inside is lower by 1 part in 105 in the diamagnet and higher by 1 part in 105 in the paramagnet (NCERT Points to Ponder 4, page 151; pages 147–148).
Q6. A paramagnetic salt has χ = 1.5 × 10−4 at 27 °C. At what temperature would its susceptibility be 6.0 × 10−4?
By Curie’s law χ = C/T (beyond NCERT), χT is constant, with T in kelvin: 27 °C ≈ 300 K, so T = 300 × 1.5 × 10−4/(6.0 × 10−4) = 75 K, approximately −198 °C.
Q7. Iron has about 8.5 × 1028 atoms per cubic metre. How many atoms are there in a domain that is a cube 1 µm across?
V = (10−6 m)3 = 10−18 m3, so N = 8.5 × 1028 × 10−18 ≈ 8.5 × 1010, about 1011 atoms, the number NCERT quotes for a domain (NCERT page 149).
Q8. Besides diamagnetic, paramagnetic and ferromagnetic materials, which other types of magnetic material does NCERT name?
Ferrimagnetic, anti-ferromagnetic and spin glass materials, whose properties NCERT calls exotic (NCERT Points to Ponder 7, page 152).
Q9. A superconductor is described as perfectly diamagnetic. Give its χ, μr and μ, and say what happens to a magnet held just above it.
In the ideal bulk Meissner state below the relevant critical limits, χ = −1, μr = 0 and μ = 0: the field is expelled apart from a thin surface penetration layer. The superconductor repels the magnet and, by Newton’s third law, is repelled by it; NCERT notes that superconducting magnets can be used to run magnetically levitated trains (NCERT page 148; Points to Ponder 5, page 152).
Q10. A paramagnetic sample has M = 8 A/m in a field of 0.6 T at 4 K. Find M in a field of 0.2 T at 16 K.
Assuming independent localised moments remain unsaturated and obey Curie’s law (beyond NCERT), M is proportional to B/T. The field falls to one third and T rises 4 times, so M = 8/(3 × 4) ≈ 0.67 A/m.
Q11. Small rods of bismuth and of aluminium are hung freely, one at a time, between the poles of a strong magnet, where the field is strongest along the line joining the poles. How does each rod settle?
Aluminium (paramagnetic) moves towards stronger field, so its rod turns along the field. Bismuth (diamagnetic) moves towards weaker field, so its rod turns across the field (reasoned from NCERT pages 147–148).