CUET UG Physics Booster Test 2-Magnetization and Material Intensity

According to NCERT, the fundamental origin of magnetism in matter is associated with the motion of electrons within atoms. When an electron revolves around the nucleus, it constitutes a moving charge and therefore behaves like a tiny current-carrying loop. Every current loop possesses a magnetic dipole moment, known as the orbital magnetic moment. These orbital magnetic moments contribute to the magnetic properties of atoms and, collectively, to the magnetic behaviour of materials. The magnetic moments of individual atoms combine vectorially to produce the net magnetic moment of a substance. This concept forms the basis for understanding diamagnetism, paramagnetism and ferromagnetism. Therefore, the statement that orbiting electrons are equivalent to current-carrying loops possessing orbital magnetic moments is correct and represents the NCERT explanation for the origin of magnetism.

NCERT explains that in diamagnetic substances, the magnetic moments associated with individual electrons cancel one another, resulting in zero net magnetic moment for each atom in the absence of an external magnetic field. When a magnetic field is applied, small changes occur in the orbital motion of electrons. Electrons whose orbital magnetic moments oppose the applied field tend to speed up, while those aligned with the field slow down. This imbalance produces a small induced magnetic moment opposite to the direction of the applied magnetic field. As a consequence, diamagnetic substances are weakly repelled by magnetic fields and tend to move from regions of stronger magnetic field to weaker magnetic field. Therefore the statement claiming that the resultant magnetic moment is non-zero before applying the field is incorrect.

Magnetisation is defined by NCERT as the net magnetic moment per unit volume of a material. If the total magnetic moment of a sample is represented by m_(net)and the volume of the sample is V, then magnetisation is given by M=m_(net)/V This definition remains valid regardless of whether the magnetic moments are partially aligned or perfectly aligned. In the situation described, all atomic magnetic moments are aligned in the same direction, resulting in the maximum possible net magnetic moment. However, the definition of magnetisation remains unchanged. Magnetisation therefore represents the concentration of magnetic moment within the material. The greater the alignment of atomic dipoles, the larger the value of m_(net)and hence the larger the magnetisation. Therefore option C correctly represents the mathematical expression for magnetisation.

Magnetic moment is a measure of the strength and orientation of a magnetic dipole. Its SI unit is A m² and therefore its dimensions are [L^2A]. Magnetisation is defined as magnetic moment per unit volume. Since volume has dimensions [L^3], the dimensions of magnetisation become [L^(-1)A]. Thus magnetic moment corresponds to item c, magnetisation corresponds to item d, the quantity having dimensions [L^2A]corresponds to magnetic moment, and the quantity having dimensions [L^(-1)A]corresponds to magnetisation. Understanding the dimensional relationship between these quantities is important because many NCERT numerical and conceptual questions are based on unit analysis. Therefore the correct matching is 1-c, 2-d, 3-a and 4-b.

For a long empty-core solenoid carrying current I with n turns per unit length, NCERT gives the magnetic field as B_0=μ_0nI This field arises solely because of the electric current flowing through the turns of the solenoid and therefore represents the contribution of the external current. Since the solenoid is assumed to have an empty core, the magnetic field is not determined by any magnetic material. Furthermore, B_0 is a physical magnetic field measured in tesla and is certainly not dimensionless. The expression shows that the field depends on the permeability of free space, current and turn density. Therefore statements 1 and 3 are correct, while statements 2 and 4 are incorrect. Hence option B is the correct answer.

When a magnetic material is placed inside a solenoid, the magnetic moments of atoms tend to align with the externally applied magnetic field. This alignment produces an additional magnetic field within the material. According to NCERT, the field due to magnetisation is proportional to the magnetisation M and is expressed as B_m=μ_0M The total magnetic field inside the material is obtained by combining the externally applied field represented by magnetic intensity H and the contribution arising from the material itself. Thus, B=μ_0(H+M) This relation is important because it separates the effects of external currents from the magnetic response of the material. A magnetic core generally enhances the magnetic field inside the solenoid rather than cancelling it. Therefore statements 1, 2 and 3 are correct, while statement 4 is incorrect. Hence option A is the correct answer.

One of the major advantages of expressing the magnetic field inside a material as B=μ_0(H+M) is that it clearly distinguishes between two physically different contributions. The quantity H represents the magnetic intensity produced by external free currents such as those flowing through a solenoid. The quantity M represents the magnetisation produced by the alignment of atomic magnetic moments within the material. By separating these two effects, the equation allows physicists to analyse the role of the material independently from the role of external sources. This approach is especially useful when comparing different magnetic materials because each material responds differently to the same applied magnetic intensity. The expression therefore provides a convenient framework for understanding magnetic susceptibility, permeability and material behaviour. Hence option C correctly describes the advantage of this representation.

For many magnetic materials subjected to moderate magnetic fields, NCERT assumes a linear relationship between magnetisation and magnetic intensity. This relationship is written as M=χH where χis the magnetic susceptibility of the material. Magnetic susceptibility indicates how readily a material becomes magnetised when exposed to an external magnetic field. If the value of χis large, the material develops a stronger magnetisation for the same applied magnetic intensity. This proportional relationship simplifies the analysis of magnetic materials and forms the basis for deriving expressions involving permeability and relative permeability. Since magnetisation increases proportionally with magnetic intensity in linear magnetic materials, option C is correct.

The required relation is H=B/μ_0-M Substituting the given values, H=1.256×10^(-3)/1.256×10^(-6)-500H=10^3-500H=1000-500H=500 A m^(-1) The unit remains A m⁻¹ because both B/μ_0 and M possess identical dimensions. This calculation demonstrates how magnetic intensity is obtained by removing the material contribution from the total magnetic field. Therefore the correct answer is 500 A m⁻¹.

In dimensional analysis, addition or subtraction is possible only between quantities having identical dimensions. The magnetic field B and magnetisation M do not possess the same dimensions. However, when B is divided by the permeability of free space μ_0, the resulting quantity acquires the dimensions [L^(-1)A] which are the same as the dimensions of magnetisation M and magnetic intensity H. This dimensional transformation is precisely why the expression H=B/μ_0-M is physically meaningful. Without dividing by μ_0, the subtraction would violate the rules of dimensional consistency. Therefore option A correctly explains the dimensional basis of the equation.

Magnetic susceptibility (χ)is a measure of how strongly a material responds to an externally applied magnetic field. According to NCERT, the relationship between magnetisation M and magnetic intensity H for a linear magnetic material is M=χH Both magnetisation and magnetic intensity have the same SI unit, A m⁻¹. Therefore, χ=M/H Since the numerator and denominator possess identical units and dimensions, the units cancel completely. As a result, magnetic susceptibility has no dimensions and no SI unit. This property makes susceptibility a convenient quantity for comparing magnetic responses of different materials. Positive values indicate paramagnetic behaviour, negative values indicate diamagnetic behaviour, and very large positive values indicate ferromagnetic behaviour. Hence option B correctly explains why susceptibility is dimensionless.

Magnetic susceptibility is an important parameter used to classify magnetic materials. According to NCERT, paramagnetic materials possess small positive susceptibility values because they become weakly magnetised in the direction of the applied magnetic field. Diamagnetic materials possess small negative susceptibility values because the induced magnetic moment opposes the applied field. Ferromagnetic materials exhibit very large positive susceptibility values, often many orders of magnitude greater than unity, because of strong cooperative alignment of atomic magnetic moments. Superconductors, however, do not have χ=+1. Instead, they exhibit perfect diamagnetism and effectively expel magnetic fields from their interiors. Therefore statements 1, 2 and 3 are correct, whereas statement 4 is incorrect. Hence option A is the correct answer.

According to NCERT, the relationship between relative magnetic permeability and magnetic susceptibility is μ_r=1+χ Given, χ=-10^(-5) Substituting, μ_r=1+(-10^(-5))μ_r=1-10^(-5)μ_r=0.99999 Since the susceptibility is negative, the material is diamagnetic. Diamagnetic materials possess relative permeability values slightly less than unity. The result is therefore consistent with the physical behaviour of diamagnetic substances. Hence the correct answer is 0.99999.

Relative magnetic permeability (μ_r)measures how easily a material permits magnetic field lines compared with free space. In electrostatics, the dielectric constant indicates how a medium responds to an electric field relative to vacuum. Similarly, relative magnetic permeability describes how a magnetic material responds to a magnetic field relative to free space. Thus μ_r serves as the magnetic analogue of dielectric constant. Since it is defined as the ratio of two permeabilities, μ_r=μ/μ_0 it is dimensionless. Paramagnetic substances have values slightly greater than unity, diamagnetic substances have values slightly less than unity, and ferromagnetic substances have values much greater than unity. Therefore option D is the correct statement.

Absolute magnetic permeability (μ)is related to the permeability of free space (μ_0)through the equation μ=μ_0μ_r Since relative permeability (μ_r)is dimensionless, it contributes no dimensions to the product. Consequently, all dimensions and units of absolute permeability are inherited directly from μ_0. The SI unit of permeability is T m A^(-1) and its dimensions are [MLT^(-2)A^(-2)] These dimensions originate entirely from the permeability of vacuum. Relative permeability merely modifies the numerical value according to the magnetic properties of the material. Therefore option C is correct.

According to NCERT, the absolute magnetic permeability of a material is related to susceptibility through μ=μ_0(1+χ) Hence item 1 corresponds to item a. The magnetic field inside a linear magnetic material is given by B=μH Therefore item 2 corresponds to item c. Permeability expressed through susceptibility represents how magnetic response modifies the vacuum permeability, corresponding to item b. The magnetic field in a linear magnetic material depends directly on both permeability and magnetic intensity, corresponding to item d. These relations form the basis of magnetic material analysis and are widely used in numerical and conceptual problems. Therefore the correct matching is 1-a, 2-c, 3-b and 4-d.

The magnetic field inside a magnetic material is given by B=μH where μ=μ_0μ_r Substituting the given values, μ=(4π×10^(-7))(400)μ=1.6π×10^(-4) Now, B=μHB=(1.6π×10^(-4))(2000)B=3.2π×10^(-1)B≈1.0 T Thus the magnetic field inside the core is approximately 1 tesla. This demonstrates how a material with high relative permeability greatly enhances the magnetic field produced by the same magnetic intensity.

For a linear magnetic material, NCERT gives M=χH where χis magnetic susceptibility. The relation between susceptibility and relative permeability is μ_r=1+χ Rearranging, χ=μ_r-1 Substituting this into the magnetisation equation gives M=(μ_r-1)H The subtraction of 1 arises because relative permeability includes the contribution of free space. Magnetisation, however, depends only on the material's additional response beyond vacuum behaviour. Therefore (μ_r, 1)appears naturally when expressing magnetisation in terms of relative permeability. Hence option D is correct.

The permeability of free space is one of the fundamental constants used in electromagnetism. According to NCERT, μ_0=4π×10^(-7) T m A^(-1) Its dimensions are [MLT^(-2)A^(-2)] In vacuum, where magnetisation is absent, the relation between magnetic field and magnetic intensity becomes B=μ_0H This equation shows that magnetic field is directly proportional to magnetic intensity in free space. Since μ_0 possesses both dimensions and units, it is not dimensionless. Therefore statements 1, 2 and 4 are correct, while statement 3 is incorrect.

The standard conversion between Gauss and Tesla is 1 Gauss=10^(-4) T Given, B=0.35 Gauss Multiplying by the conversion factor, B=0.35×10^(-4) TB=3.5×10^(-5) T This value is consistent with the typical strength of the Earth's magnetic field, which is usually of the order of 10^(-5)tesla. Such values are commonly used in NCERT examples involving geomagnetism and magnetic measurements. Therefore the correct answer is 3.5×10^(-5) T.