Tiêu đề 05. MAGNETISM and MATTER.pdf ✅

20. () : Explana on We have, or For a solenoid of -turns per unit length and current , Magne c moment 21. () : Explana on Super conductors are diamagne c below (Here means temperature at which nor‐ mal conductor becomes super conductor). When superconductors reach their cri cal temperature , the Meissner effect expels magne c fields, causing magne c repulsion. This repulsion, seen when a magnet hoveres above a cooled superconductor, is due to the induced magne c field opposing the applied field. So correct op on is (1). 22. () : Explana on Given, Dipole moment of the earth ? 23. () : Explana on Magne c suscep bility is indeed a pure number, as it represents the ra o of the inten‐ sity of magne za on to the magne c in‐ tensity of the magne zing field. is unit-less and dimensionless number. The magne c suscep bility of vacuum (free space) is exactly zero, not one, as there is no magne za on in vacuum. So correct op on is (3). 24. () : Explana on 25. () : Explana on Work done, So, correct op on is (4). 26. () : Explana on Diamagne sm is when a material acquires a magne sa on in the opposite direc on to the applied magne c field. Diamagne sm is caused by orbital mo on of electrons. So op‐ on (3) is correct. 27. () : Explana on Paramagne c substances are weakly a racted to an external magne c field. When placed in a magne c field, the magne c dipoles of the atoms or molecules in paramagne c materials align themselves in the direc on of the exter‐ nal magne c field, resul ng in weak magne ‐ za on. This alignment makes paramagne c substances weakly a racted to the magne c field. The weak a rac on of paramagne c sub‐ stances in a magne c field is due to the fact that the magne c dipoles within these mate‐ rials align along the direc on of the external magne c field, but the alignment is rela vely weak compared to ferromagne c materials. This alignment results in weak magne za on and, consequently, weak a rac on to the magne c field. The reason accurately explains why paramag‐ ne c substances are poorly a racted to a magne c field, making it the correct explana‐ on for the asser on. Therefore, the answer is (1) Both Asser on and Reason are correct, and Reason is the correct explana on of Asser on. B = μ0H + μ0M ⇒ M = B − μ0H μ0 M = μH − μ0H μ0 = ( − 1) H μ μ0 M = (μr − 1) H n i H = ni ∴ M = (μr − 1) ni = (1000 − 1) × 500 × 0.5 M = 2.5 × 10 5Am −1 m = MV = 2.5 × 10 5 × 10 −4 = 25Am 2 TC TC (TC) B = 4 × 10 −5 T RE = 6.4 × 10 6 m M = B = μ0 4π M d3 4 × 10 −5T = ∴ M ≅10 23 4π×10 Am2 −7×M 4π×(6.4×10 6 3 ) (χ) (I) (H) χ = = ( ) I M A/m A/m ⇒ χ B = μ0 4π 2M d 3 = = 3 × 10 −8 T 10 −7×2×0.1×12 2 3 W = MB(1 − cos θ) θ = 90 ∘ ∴ W = MB
28. () : Explana on Here; The me taken by the dipole to complete 20 oscilla ons 29. () : Explana on Time period of dipole in a uniform magne c field is . Since magne c moment decreases with increase in temperature hence me period increases. 30. () : Explana on Magne c field of earth is due to movement of molten metals which has charged par cles. With increase in temperature, the magne c moment of magnet decreases. 31. () : Explana on 32. () : Explana on As we know for circula ng electron magne c moment and angular momentum From equa on (1) and (2), 33. () : Explana on 34. () : Explana on Horizontal component of earth's magne c field is given by Now, 35. () : Explana on Time period of dipole in a uniform magne c field is . If is an iden cal bar magnet then me period of system will be 36. () : Explana on Conceptual Ques on 37. () : Explana on According to Curie's law 38. () : Explana on Adding a so iron core enhances a moving coil galvanometer's sensi vity by concentrat‐ ing the magne c field. Also, so iron is easily magne zed and demagne zed due to its high magne c permeability. So correct op on is (3). 39. () : Explana on T = 2π√ I MB B = 2 × 10 −2 T, 1 = 12 × 10 −6 kg m2 M = 6 × 10 −2Am2 T = 2π√ = ≃ 0.6 s 12×10 −6 6×10 −2×2×10 −2 2×3 10 = 0.6 × 20 = 12 s T ∝ 1 √M T tan θ1 = tan θ cos α ⇒ tan θ2 = = tan θ cos(90−α) tan θ sin α ⇒ sin 2α + cos 2α = 1 cot 2θ2 + cot 2θ1 = cot 2θ M = iπr 2 = = evr (1) eωπr 2 2π 1 2 J = mvr (2) M = eJ 2m BH = B cos δ B = = = 5 × 10 −5 T BH cos δ 3×10 −5 3/5 BH = B cos δ or cos δ = = = ∴ = sec δ = BH B 0.3 0.5 3 5 1 cos θ 5 3 tan δ = √sec 2 δ − 1 = √( ) 2 − 1 5 3 = √ − 1 = ⇒∴ δ = tan −1 25 9 4 3 4 3 T = 2π√ I MBH Q T ′ = 2π√ = T 2I (2M)BH ⇒ χ ∝ 1 T χ1 T1 = χ2 T2 = ( ) 3 = ( ) 3 = ( ) 3 = M1 M2 d1 d2 15 20 3 4 27 64