Magnetism And Matter Class 12 Physics Chapter 5 Notes

Magnetism and Matter Class 12 Physics Chapter 5 Notes

Magnetism

Universality of Magnetic Phenomena: Magnetic phenomena exist everywhere in the universe, from distant galaxies to atoms. These phenomena involve the presence of magnetic fields generated by moving charges or electric currents.
Historical Background: The discovery of the relationship between electric currents and magnetic fields dates back to the early 19th century and is attributed to scientists like Oersted, Ampere, Biot, and Savart. The term “magnet” is derived from “magnesia,” an island in Greece where magnetic ores were found around 600 BC.
Earth as a Magnet: The Earth itself behaves like a magnet, with its magnetic field pointing approximately from the geographic south to the north. This natural magnetism is why compass needles point north.
Bar Magnet: A bar magnet, when freely suspended, aligns itself in the north-south direction. The end pointing to the geographic north is called the north pole, and the end pointing to the geographic south is called the south pole.
Magnetic Poles and Interaction: Like poles of magnets (either north or south) repel each other, while opposite poles (north and south) attract each other. There is no way to isolate a single magnetic pole; breaking a magnet results in two smaller magnets with weaker properties.
Materials and Magnetism: Materials can be classified based on their magnetic properties. There are three main categories: paramagnetic, diamagnetic, and ferromagnetic substances. Each category exhibits different behaviors when placed in a magnetic field.
Permanent Magnets: It is possible to create magnets from materials like iron and its alloys. These are known as permanent magnets because they retain their magnetic properties even when removed from external magnetic fields.
Electromagnets: Electromagnets are temporary magnets created by passing an electric current through a coil of wire. They are widely used in various applications, including electric appliances, industrial machinery, and scientific instruments.

Characteristics and properties of magnetic field lines generated by a bar magnet or a current-carrying solenoid

Continuous Closed Loops: Magnetic field lines form continuous closed loops around a magnet or a solenoid. Unlike electric field lines in an electric dipole, which start from a positive charge and end on a negative charge or extend to infinity, magnetic field lines do not have starting or ending points.
Tangent Direction: The tangent to a magnetic field line at a particular point indicates the direction of the net magnetic field (B) at that point. In other words, the magnetic field vector is tangent to the field line at any given location.
Strength of Field: The density of magnetic field lines crossing a unit area is proportional to the strength (magnitude) of the magnetic field at that location.
Non-Intersecting Lines: Magnetic field lines do not intersect or cross each other. If they were to intersect, it would lead to ambiguity in determining the direction of the magnetic field at the point of intersection.
Visualization: Magnetic field lines can be visualized and plotted in various ways. One common method is to place a small magnetic compass needle at different positions and observe its orientation. The direction in which the compass needle aligns itself indicates the direction of the magnetic field at those points.

Treating a bar magnet as an equivalent solenoid with circulating currents

Magnetic Field Lines Resemblance: The magnetic field lines around a bar magnet and a current-carrying solenoid exhibit a resemblance. This resemblance suggests that a bar magnet can be conceptualized as having a large number of circulating currents, similar to a solenoid. When a bar magnet is cut in half, it is akin to cutting a solenoid, resulting in two smaller solenoids with reduced magnetic properties. The field lines remain continuous, emerging from one face of the magnet (or solenoid) and entering the other face.
Verification with Compass Needle: The analogy between a bar magnet and a solenoid can be tested by observing the behavior of a small compass needle in the vicinity of both objects. It is noted that the deflections of the compass needle are similar in both cases, further supporting the analogy.
Axial Magnetic Field of a Solenoid: The passage mentions that the axial magnetic field of a finite solenoid at large distances follows a formula represented as:
- B=4μ0m/3πr^3
- where B is the magnetic field, m is the magnetic moment, μ0 is the permeability of free space, and r is the distance from the solenoid. This formula describes the far axial magnetic field of a solenoid.
Bar Magnet Equivalence: The axial magnetic field of a solenoid is similar to the magnetic field of a bar magnet at a distance. Therefore, it is concluded that the magnetic moment of a bar magnet is equal to the magnetic moment of an equivalent solenoid that generates the same magnetic field.

Magnetic potential energy of a small compass needle in a uniform magnetic field

Torque on the Needle: The torque (t) acting on the compass needle due to the magnetic field is given by
- t=m×B,
- where m is the magnetic moment of the needle, and B is the magnetic field.
- The magnitude of this torque can also be expressed as t=mBsinθ, where θ is the angle between the magnetic moment vector (m) and the magnetic field vector (B). This torque acts as a restoring torque, trying to align the needle with the magnetic field.
Magnetic Potential Energy: Similar to electrostatic potential energy, magnetic potential energy (Um) can be defined for the magnetic interaction. The expression for magnetic potential energy is given by:
- Um=−m⋅B.
- This expression describes the magnetic potential energy of the compass needle in the presence of the magnetic field. It is negative and depends on the orientation of the magnetic moment relative to the magnetic field.
Zero of Potential Energy: The zero of potential energy can be chosen arbitrarily. Setting the constant of integration to zero means fixing the zero of potential energy at θ=90∘, which corresponds to when the needle is perpendicular to the magnetic field.
Potential Energy at Different Orientations: The potential energy is minimum (equal to −mB) when θ=0∘, which is the most stable orientation where the magnetic moment aligns with the magnetic field. Conversely, the potential energy is maximum (equal to +mB) when θ=180∘, representing the most unstable orientation where the magnetic moment points in the opposite direction to the magnetic field.

Analogy between the equations for magnetic fields generated by a bar magnet and electric fields generated by an electric dipole

Electric Dipole to Magnetic Dipole: The equation for the electric field (E) due to an electric dipole with dipole moment (p) is compared to the magnetic field (B) due to a magnetic dipole with magnetic moment (m). The substitutions are as follows:
- E (electric field) is replaced with B (magnetic field).
- p (electric dipole moment) is replaced with m (magnetic moment).
- �0ϵ0 (electric constant, also known as vacuum permittivity) is replaced with μ0 (magnetic constant, also known as vacuum permeability), with the appropriate conversion factors.
Resultant Magnetic Fields: The author then provides expressions for the magnetic field at large distances from a bar magnet, making these substitutions:
- The equatorial magnetic field (BE) of a bar magnet at a distance (r) when r is much greater than the size of the magnet (l) is given by: BE=μ0m/4πr
- The axial magnetic field (BA) of a bar magnet at a distance (r) when r is much greater than the size of the magnet (l) is given by:
- BA=μ02m/4πr^3

These equations describe the behavior of the magnetic field produced by a bar magnet at significant distances from the magnet and draw parallels with the behavior of electric fields produced by electric dipoles. This analogy helps in understanding the magnetic properties of bar magnets in terms of their magnetic moments.

Magnetism and Gauss’s law

Gauss’s Law for Electrostatics: Gauss’s law states that the electric flux through a closed surface (ΦE) is equal to ϵ0q, where q is the electric charge enclosed by the surface, and ϵ0 is the electric constant (vacuum permittivity).
Gauss’s Law for Magnetism: The author introduces Gauss’s law for magnetism. Unlike Gauss’s law for electrostatics, which involves electric charges (q), Gauss’s law for magnetism deals with magnetic fields (B). The law states that the net magnetic flux through any closed surface is always zero. In other words, there are no sources or sinks of magnetic field lines, and the total number of magnetic field lines entering a closed surface is equal to the number exiting it.

This distinction arises from the fact that magnetic monopoles (isolated magnetic poles) are not known to exist. In magnetism, there are no individual magnetic charges (analogous to electric charges), and magnetic phenomena are explained in terms of arrangements of magnetic dipoles and current loops.

Magnetization and Magnetic intensity

Magnetization (M): Magnetization is defined as the net magnetic moment per unit volume of a material. In a bulk material, the magnetic moments of individual electrons add up vectorially, resulting in a net magnetic moment for the material. Magnetization (M) is expressed in units of Am⁻¹ (ampere per meter).
Magnetic Field Inside a Solenoid: The magnetic field (B₀) inside a long solenoid with n turns per unit length and carrying a current I is given by the expression B₀ = μ₀nI, where μ₀ is the permeability of vacuum.
Effect of Material on Magnetic Field: If the interior of the solenoid is filled with a material that has a non-zero magnetization (M), the total magnetic field (B) inside the solenoid will be greater than B₀. This additional field (Bm) contributed by the material is proportional to the magnetization (M) and is expressed as Bm = μ₀M.
Magnetic Intensity (H): Magnetic intensity (H) is defined as a vector field and represents the contribution of external factors, such as the current in a solenoid, to the magnetic field. It is also measured in units of Am⁻¹.
Relationship Between B, H, and M: The total magnetic field (B) inside a material can be expressed as B = μ₀(H + M), where H is the magnetic intensity. This equation partitions the contribution to the total magnetic field into two parts: one due to external factors (H) and the other due to the specific nature of the magnetic material (M).
Magnetic Susceptibility (χ): The magnetic susceptibility (χ) is a dimensionless quantity that measures how a magnetic material responds to an external magnetic field. It is positive and small for paramagnetic materials and negative and small for diamagnetic materials. The magnetic susceptibility is related to the ratio of M to H.
Relative Magnetic Permeability (mr): The relative magnetic permeability (mr) is a dimensionless quantity that represents how much a material can be magnetized compared to a vacuum. It is related to the magnetic susceptibility as mr = 1 + χ.
Magnetic Permeability (m): Magnetic permeability (m) is the property that quantifies how easily a material can be magnetized. It has the same dimensions and units as μ₀ and is related to the relative magnetic permeability as m = μ₀mr.

Diamagnetism

Diamagnetic Substances: Diamagnetic substances are materials that tend to move from regions of stronger external magnetic fields to weaker ones. In contrast to how a magnet attracts magnetic materials like iron, a diamagnetic substance is repelled by a magnetic field.
Behavior in an External Magnetic Field: When a bar of diamagnetic material is placed in an external magnetic field, the magnetic field lines are repelled or expelled from the material, causing a reduction in the magnetic field strength inside the material. This reduction is usually slight, typically on the order of one part in 10^5.
Response to Non-Uniform Magnetic Fields: In the presence of a non-uniform magnetic field, a diamagnetic bar will tend to move from regions of high magnetic field strength to regions of low field strength.
Explanation of Diamagnetism: Diamagnetism can be explained by the behavior of electrons in the atoms of the material. Electrons in orbit around the nucleus possess orbital angular momentum and, consequently, orbital magnetic moments. Diamagnetic materials are those in which the net magnetic moment of the atoms is zero. When an external magnetic field is applied, it induces currents in the electrons’ orbits, in accordance with Lenz’s law. This induced current results in a net magnetic moment in the opposite direction to the applied field, leading to repulsion.
Examples of Diamagnetic Materials: Some examples of diamagnetic materials include bismuth, copper, lead, silicon, nitrogen (at standard temperature and pressure), water, and sodium chloride. Diamagnetism is present in all substances to some degree, but its effects are typically weak and can be overshadowed by other magnetic effects like paramagnetism and ferromagnetism.
Superconductors: Superconductors are a class of materials that exhibit both perfect electrical conductivity and perfect diamagnetism when cooled to very low temperatures. In superconductors, the magnetic field lines are completely expelled, resulting in strong diamagnetic behavior. Superconducting magnets are used in various applications, including magnetically levitated superfast trains, and they demonstrate the Meissner effect, named after its discoverer.

Diamagnetism is one of the fundamental magnetic behaviors exhibited by materials and is characterized by the tendency of diamagnetic substances to repel magnetic fields.

Paramagnetism

Paramagnetic Substances: Paramagnetic substances are materials that become weakly magnetized when exposed to an external magnetic field. They are attracted to regions of strong magnetic fields and tend to move from areas of weak magnetic fields.
Individual Atomic Dipole Moments: In paramagnetic materials, individual atoms (or ions or molecules) possess their own permanent magnetic dipole moments. However, due to the constant and random thermal motion of these atoms, there is typically no net magnetization observed in the absence of an external magnetic field.
Alignment in an External Field: When a paramagnetic material is subjected to an external magnetic field, provided the field is strong enough and the temperature is sufficiently low, the individual atomic dipole moments can align themselves in the same direction as the external field. This alignment results in an enhancement of the magnetic field inside the material.
Behavior in External Field: In the presence of an external magnetic field (denoted as B0), the field lines within a paramagnetic material become concentrated and intensified. This causes the material to be attracted to the magnet or the region with a stronger magnetic field. When placed in a non-uniform magnetic field, the paramagnetic bar will tend to move from areas of weaker magnetic field to stronger ones.
Examples of Paramagnetic Materials: Some examples of paramagnetic materials include aluminum, sodium, calcium, oxygen (at standard temperature and pressure), and copper chloride. The paramagnetic behavior of a material depends on both the specific material itself and its temperature. As the strength of the external magnetic field is increased or the temperature is lowered, the degree of magnetization increases until it reaches a saturation point, at which all the atomic dipoles are perfectly aligned with the field.

Paramagnetism is characterized by the weak attraction of paramagnetic substances to magnetic fields and is driven by the alignment of individual atomic magnetic moments with an external magnetic field when conditions are suitable.

Ferromagnetism

Ferromagnetic Substances: Ferromagnetic substances are materials that become strongly magnetized when exposed to an external magnetic field. They exhibit a strong attraction to regions with a strong magnetic field and tend to move from areas of weak magnetic fields.
Atomic Dipole Moments: Similar to paramagnetic materials, individual atoms (or ions or molecules) in a ferromagnetic material possess magnetic dipole moments of their own. However, the unique characteristic of ferromagnetic materials is the interaction between these atomic dipole moments. This interaction causes them to spontaneously align themselves in a common direction over macroscopic regions known as domains.
Domains: Domains are small regions within a ferromagnetic material where atomic magnetic moments are aligned in the same direction. Each domain possesses its own net magnetization. The typical size of a domain is about 1 mm, and it contains roughly 10^11 atoms. Initially, in the absence of an external magnetic field, the magnetization within domains varies randomly, resulting in no bulk magnetization.
Alignment in an External Field: When an external magnetic field (denoted as B0) is applied, the domains within the ferromagnetic material begin to align themselves in the direction of B0. Simultaneously, the domains oriented in the direction of B0 grow in size, creating a strong alignment of atomic magnetic moments. This phenomenon is observable under a microscope when a liquid suspension of powdered ferromagnetic substance is used.
High Concentration of Field Lines: In a ferromagnetic material, the magnetic field lines become highly concentrated when exposed to an external magnetic field. Consequently, the material exhibits a strong attraction to regions with a high magnetic field. In non-uniform magnetic fields, the ferromagnetic sample tends to move toward regions of higher field strength.
Permanent and Soft Ferromagnetic Materials: Some ferromagnetic materials retain their magnetization even after the external magnetic field is removed. These are known as hard ferromagnetic materials and are used in the production of permanent magnets. Soft ferromagnetic materials, on the other hand, lose their magnetization when the external field is removed. An example of a hard ferromagnetic material is Alnico, while soft iron is an example of a soft ferromagnetic material.
Temperature Dependence: The ferromagnetic properties of a material are temperature-dependent. At sufficiently high temperatures, a ferromagnetic substance can transition into a paramagnetic state. This transition occurs because the domain structure disintegrates with increasing temperature, causing the magnetization to disappear. The change in magnetization with temperature is gradual.

Ferromagnetism is characterized by the strong attraction and alignment of atomic magnetic moments within domains when exposed to an external magnetic field. This property has significant applications, including the production of permanent magnets used in compass needles and various industrial applications.