CUET UG Physics Booster Test 3-Magnetization and Material Intensity

NCERT explains that magnetism originates from the orbital and spin motions of electrons within atoms. In some atoms, the magnetic moments of electrons cancel each other, producing zero resultant magnetic moment. Such atoms often exhibit diamagnetic behaviour. Applying an external magnetic field to these atoms can induce a weak magnetic moment, but this does not transform the material into a ferromagnet. Ferromagnetism arises due to strong cooperative interactions between neighbouring atomic magnetic moments and the formation of magnetic domains. It is an intrinsic property of certain materials such as iron, cobalt and nickel. Therefore, merely applying an external field to atoms with zero resultant magnetic moment cannot create perfect ferromagnetic alignment. Hence statement C is incorrect and is the correct answer to the question.

According to NCERT, paramagnetic substances contain atoms or ions that possess permanent magnetic dipole moments. In the absence of an external magnetic field, these dipoles are oriented randomly because of continuous thermal motion. Since magnetic moment is a vector quantity, the random orientations cause the vector sum of all magnetic moments to become nearly zero. Consequently, no observable macroscopic magnetisation exists. When an external magnetic field is applied, some alignment occurs and a small positive magnetisation develops in the direction of the field. The absence of magnetisation before applying the field is therefore due to thermal disorder rather than cancellation within each atom. Hence option B correctly explains the behaviour of paramagnetic materials.

Magnetisation is defined as the net magnetic moment per unit volume of a material. Mathematically, M=m_(net)/V If heating causes the volume to increase while the net magnetic moment remains unchanged, the denominator of the expression increases whereas the numerator remains constant. As a result, the value of magnetisation decreases. Physically, the same magnetic moment becomes distributed over a larger volume, reducing the magnetic moment density. This follows directly from the NCERT definition of magnetisation. Therefore option D is correct.

Magnetisation is defined as M=m_(net)/V The SI unit of magnetic moment is A m², which corresponds to dimensions [L^2A]. Volume has dimensions [L^3]. Dividing these quantities gives [M]=[L^2A]/[L^3][M]=[L^(-1)A] This dimensional formula agrees with the SI unit A m⁻¹. Magnetisation therefore has dimensions different from magnetic flux and is certainly not dimensionless. Hence option A is correct.

For a magnetic material placed inside a solenoid, B=B_0+B_m where B_0 is the field due to external current and B_m is the field due to magnetisation of the core. Substituting the given values, 802.0=2.0+B_m Therefore, B_m=802.0-2.0B_m=800.0 mT The large value of B_m indicates strong enhancement of the magnetic field by the core material. Hence option C is correct.

According to NCERT, the magnetic field inside an empty solenoid is produced entirely by the external current and is given by B_0=μ_0nI When a magnetic material is introduced into the solenoid, alignment of atomic magnetic moments creates an additional magnetic field B_m=μ_0M The total magnetic field inside the material becomes B=B_0+B_m Therefore, B_0 corresponds to the field generated by external current, while B_m corresponds to the field generated by the magnetic response of the material. The material contribution depends on magnetisation, whereas the external contribution exists even in the absence of any magnetic material. Thus the correct matching is 1-b, 2-c, 3-a and 4-d.

Magnetic intensity H represents the magnetic field produced by external free currents. For a long solenoid carrying current I with n turns per unit length, H=nI This relation is independent of the magnetic material. The field B_m, however, originates from the magnetisation of the material and therefore cannot exist without a magnetic medium. Thus statements 2 and 3 are correct. Statement 1 is incorrect because H does not isolate the material from the external current; rather, it represents the external contribution itself. Statement 4 is incorrect because the total magnetic field depends on both magnetic intensity and magnetisation according to B=μ_0(H+M) Hence option D is correct.

The magnetic field contribution B_m originates from the collective alignment of atomic magnetic moments within a material. According to NCERT, B_m=μ_0M This equation shows a direct proportionality between magnetisation and the field produced by the material. The total magnetic field inside the material is obtained by combining the field due to the external current and the field due to magnetisation: B=B_0+B_m Thus statements 1, 2 and 3 are correct. Statement 4 is incorrect because paramagnetic materials do develop magnetisation when placed in an external magnetic field. Consequently, B_m is not zero in paramagnets. Hence option A is correct.

For a perfect diamagnetic material such as a superconductor, B=0 Using the NCERT relation, B=μ_0(H+M) Substituting B=0, 0=μ_0(H+M) Since μ_0≠0, H+M=0 Therefore, H=-M This result indicates that the magnetisation exactly opposes the externally applied magnetic intensity. Such complete opposition is characteristic of perfect diamagnetism and explains why magnetic flux is expelled from superconductors. Hence option B is correct.

In physics, addition is possible only between quantities possessing the same dimensions and representing compatible physical quantities. Magnetic intensity H and magnetisation M are both vector quantities. Their SI unit is A m^(-1) and their dimensional formula is [L^(-1)A] Because they share identical dimensions and vector nature, they can be added directly inside the expression B=μ_0(H+M) The permeability of free space μ_0 then converts the resulting quantity into magnetic field B. If H and M possessed different dimensions, the equation would violate dimensional consistency. Therefore option A correctly explains the mathematical basis of the equation.

The relation M = χH is a linear approximation used for many magnetic materials under ordinary magnetic field strengths. Here, χ represents magnetic susceptibility and indicates how strongly a material becomes magnetised in response to an applied magnetic field H. This relation forms the basis for deriving μᵣ = 1 + χ and is valid for diamagnetic and paramagnetic substances and for ferromagnets over a limited range of fields. However, ferromagnetic materials exhibit magnetic saturation at high field strengths. Once saturation is reached, further increases in H do not produce proportional increases in M. Therefore, the linear relation M = χH is no longer valid. Hence option D is the incorrect statement.

Superconductors exhibit the Meissner effect, in which magnetic field lines are completely expelled from the interior of the material. As a result, the magnetic susceptibility becomes χ = -1. Using the relation μᵣ = 1 + χ, we obtain μᵣ = 0. Therefore, statements 1, 2 and 3 are correct. Superconductors are not perfect insulators; instead, they are perfect conductors with zero electrical resistance below the critical temperature. Hence statement 4 is incorrect. The complete exclusion of magnetic fields is one of the most remarkable properties of superconductivity and distinguishes superconductors from ordinary diamagnetic materials.

Given: B = 0.5B₀ and B = μᵣB₀ Therefore: μᵣ = 0.5 Using the NCERT relation: μᵣ = 1 + χ 0.5 = 1 + χ χ = -0.5 The negative value indicates diamagnetic behaviour. The reduction of magnetic field inside the material signifies that the induced magnetisation opposes the applied field. Hence the magnetic susceptibility is -0.5.

Diamagnetic materials possess a small negative susceptibility. Since: μᵣ = 1 + χ and -1 ≤ χ < 0, adding χ to unity gives: 0 ≤ μᵣ < 1 For ordinary diamagnetic materials, μᵣ remains slightly less than 1. This means the material weakly opposes the magnetic field and allows magnetic flux less readily than vacuum. Only in the limiting case of a perfect diamagnet such as a superconductor does μᵣ become exactly zero. Therefore, for general diamagnetic materials, μᵣ lies strictly between 0 and 1.

For vacuum: χ = 0 Using the permeability relation: μ = μ₀(1 + χ) μ = μ₀(1 + 0) μ = μ₀ Thus the absolute permeability of vacuum is exactly equal to the permeability of free space itself. This quantity is a universal physical constant with value 4π × 10⁻⁷ H m⁻¹.

Relative permeability μᵣ is defined as the ratio μ/μ₀ and therefore has no dimensions. It merely acts as a numerical scaling factor indicating how the permeability of a material compares with that of free space. When μᵣ is multiplied by μ₀, the resulting quantity μ acquires the same dimensions and units as μ₀. The dimensional formula of permeability is [MLT⁻²A⁻²]. Its SI unit may be written as H m⁻¹ or equivalently T m A⁻¹. Since μ = μ₀μᵣ, μ and μ₀ possess identical dimensions. Therefore statements 1, 2 and 4 are correct, whereas statement 3 is incorrect.

Magnetisation is defined as the net magnetic moment per unit volume of a material. When the magnetic core is removed from a solenoid, the region inside becomes a vacuum. Since a vacuum contains no atoms or magnetic dipoles that can align with the magnetic field, there is no magnetisation. The magnetic field produced by the solenoid current may still exist, but the contribution due to magnetised matter disappears. Therefore the magnetisation M becomes zero. This distinction between magnetic field intensity H and magnetisation M is important in understanding magnetic materials. H may exist in vacuum, but M requires matter.

For a magnetised material inside a solenoid: B = μ₀(H + M) Dividing by μ₀ gives: B/μ₀ = H + M The field due to the solenoid current alone is: B₀ = μ₀H The additional field due to magnetisation is: Bₘ = B − B₀ Thus B − B₀ directly represents the magnetic field contribution arising from the magnetised material. These relations are frequently used in deriving susceptibility and permeability expressions and help separate the effects of free currents and magnetisation.

The relation between relative permeability and susceptibility is: μᵣ = 1 + χ If μ < μ₀, then μᵣ < 1. Therefore: χ = μᵣ − 1 which must be negative. A negative susceptibility is the defining characteristic of diamagnetic substances. Such materials develop induced magnetic moments opposite to the applied magnetic field and are weakly repelled by stronger magnetic field regions. Examples include copper, silver, bismuth and water. Hence a material with μ < μ₀ must be diamagnetic and possess negative susceptibility.

The SI unit of magnetic flux density is tesla (T), while gauss is the corresponding CGS unit. The conversion factor is: 1 Tesla = 10⁴ Gauss Given: B = 0.035 T Therefore: B = 0.035 × 10⁴ Gauss = 350 Gauss Hence the equivalent magnetic flux density is 350 Gauss. Such unit conversions are frequently used when comparing magnetic field strengths expressed in SI and CGS systems. Careful application of the conversion factor avoids errors involving powers of ten.