Magnetism And Matter Class 12 Notes

Key Definitions in Magnetism

Magnetic Dipole Moment (m)

A vector quantity representing the strength and orientation of a magnetic dipole. For a bar magnet, m = pole strength × magnetic length. SI unit: Am² or JT⁻¹.

Magnetic Field Intensity (H)

Also called magnetizing field, it's the external magnetic field that magnetizes a material. It represents the ability of the field to magnetize a material. SI unit: A/m.

Magnetic Induction (B)

The total magnetic field inside a material when placed in an external magnetizing field. It is the sum of the external field and the field due to magnetization of the material. SI unit: Tesla (T).

Magnetization (M)

The net magnetic dipole moment developed per unit volume of a material when placed in a magnetizing field. It indicates how strongly a material is magnetized. SI unit: A/m.

Magnetic Susceptibility (χm)

A dimensionless quantity that measures how easily a material can be magnetized when placed in an external magnetic field. χm = M/H.

Magnetic Permeability (μ)

A measure of a material's ability to support the formation of a magnetic field within itself. μ = B/H. SI unit: Hm⁻¹ or NA⁻².

Relative Permeability (μr)

The ratio of the magnetic permeability of a material to the permeability of free space (μ₀). μr = μ/μ₀ = 1 + χm. Dimensionless.

Curie Temperature (Tc)

The specific temperature above which a ferromagnetic material loses its ferromagnetism and becomes paramagnetic.

Hysteresis

The lagging of magnetic induction (B) behind the magnetizing field (H) when a ferromagnetic material is subjected to a cycle of magnetization and demagnetization.

Earth's Magnetism and Classification of Magnetic Materials

The Earth behaves like a giant magnet, generating its own magnetic field. This field is believed to originate from the molten core of the Earth, where convective currents of metallic fluids create electric currents, which in turn produce magnetic fields (dynamo effect). The Earth's magnetic poles are not aligned with its geographic poles; the magnetic South pole is near the geographic North pole, and vice-versa. This misalignment leads to variations in the magnetic field across the Earth's surface.

To describe the Earth's magnetic field at any point, three magnetic elements of Earth are used:

1. Magnetic Declination (α): The angle between the geographic meridian and the magnetic meridian at a place. It indicates the angular difference between true North and magnetic North.
2. Magnetic Dip or Inclination (δ): The angle that the total magnetic field of the Earth makes with the horizontal plane at a given location. At the magnetic poles, the dip angle is 90°, and at the magnetic equator, it is 0°.
3. Horizontal Component (BH) of Earth's Magnetic Field: The component of the Earth's total magnetic field (BE) along the horizontal direction. If BV is the vertical component, then BE = √(BH² + BV²) and tan δ = BV/BH.

Materials respond differently to an external magnetic field, allowing them to be classified based on their magnetic properties. This behavior is determined by the atomic structure, specifically the presence and arrangement of unpaired electrons and their associated magnetic moments. The net magnetic moment of an atom arises from the orbital motion and spin of its electrons. When placed in an external field, these atomic moments align or misalign, leading to different macroscopic magnetic behaviors. The key classifications are diamagnetic, paramagnetic, and ferromagnetic materials, each with distinct characteristics regarding susceptibility, permeability, and temperature dependence. Understanding these classifications is fundamental to applied physics, from data storage to medical imaging. The concepts of magnetic intensity (H), magnetization (M), and magnetic induction (B) are interconnected by the relation B = μ₀(H + M), where μ₀ is the permeability of free space.

Comparison of Magnetic Materials

Worked Examples

• {"title":"Example 1: Magnetic Dipole Moment","description":"A bar magnet of magnetic moment 2 Am² is placed in a uniform magnetic field of 0.1 T. Calculate the work done in rotating the magnet from a position parallel to the field to a position anti-parallel to the field.","solution":"Given: Magnetic moment (M) = 2 Am², Magnetic field (B) = 0.1 T.\nInitial position θ₁ = 0° (parallel).\nFinal position θ₂ = 180° (anti-parallel).\nWork done (W) = -MB(cosθ₂ - cosθ₁)\nW = - (2)(0.1) (cos180° - cos0°)\nW = - 0.2 (-1 - 1)\nW = - 0.2 (-2)\nW = 0.4 J"}
• {"title":"Example 2: Magnetic Susceptibility and Permeability","description":"If the magnetic susceptibility of a material is 499, find its relative permeability and absolute permeability.","solution":"Given: Magnetic susceptibility (χm) = 499.\nRelative permeability (μr) = 1 + χm\nμr = 1 + 499 = 500.\nAbsolute permeability (μ) = μr × μ₀\nAssuming μ₀ = 4π × 10⁻⁷ Tm/A (permeability of free space),\nμ = 500 × 4π × 10⁻⁷ Tm/A\nμ = 2000π × 10⁻⁷ Tm/A ≈ 6.28 × 10⁻⁴ Tm/A."}

Must Remember for Exams

• Bar magnet as an equivalent solenoid: A bar magnet produces a magnetic field similar to a current-carrying solenoid. Its magnetic dipole moment is given by M = nIA, where n is turns per unit length, I is current, A is area.
• Torque on a magnetic dipole: When a magnetic dipole (moment M) is placed in a uniform magnetic field (B), the torque acting on it is τ = M × B = MB sinθ. Work done in rotating it is W = MB(cosθ₁ - cosθ₂).
• Potential energy of a magnetic dipole: U = -M · B = -MB cosθ. Minimum energy when parallel (θ=0°), maximum when anti-parallel (θ=180°).
• Gauss's Law for Magnetism: ∫ B · dA = 0. This implies that isolated magnetic poles (monopoles) do not exist; magnetic field lines are continuous and form closed loops.
• Hysteresis loop: Represents the B-H curve for ferromagnetic materials. Its area gives the energy loss per unit volume per cycle. Important terms: Retentivity (residual magnetism when H=0) and Coercivity (reverse H required to demagnetize).
• Soft iron vs. Steel: Soft iron has low retentivity and low coercivity, making it suitable for electromagnets. Steel has high retentivity and high coercivity, making it suitable for permanent magnets.
• Magnetic Shielding: Achieved by enclosing an area within a soft iron ring or shell, which diverts the magnetic field lines, protecting the interior from external magnetic fields.

Exam Strategy & Common Traps

When attempting questions from 'Magnetism And Matter', pay close attention to the vector nature of magnetic quantities like magnetic moment (M) and magnetic field (B). Always consider the direction, especially when calculating torque or potential energy. A common trap is confusing magnetic intensity (H) with magnetization (M); remember that H is the external magnetizing field, while M is the material's response. Be precise with units for each quantity. For questions involving magnetic elements of Earth, clearly define declination, dip, and horizontal component, often with diagrams. Practice drawing and interpreting hysteresis loops for both soft iron and steel, highlighting their retentivity and coercivity. Distinguish between the properties of diamagnetic, paramagnetic, and ferromagnetic materials, focusing on their susceptibility and temperature dependence. A clear understanding of the atomic origins of magnetism (paired vs. unpaired electrons) will help you answer conceptual questions effectively.

Practice Questions with Solutions

• Q: What is the significance of the area enclosed by a hysteresis loop? A: The area enclosed by a hysteresis loop represents the energy lost per unit volume per cycle of magnetization and demagnetization in a ferromagnetic material.
• Q: Why are diamagnetic materials weakly repelled by a magnetic field? A: In diamagnetic materials, orbital motion of electrons produces induced magnetic moments that oppose the external magnetic field, leading to weak repulsion.
• Q: Define magnetic declination and magnetic dip. A: Magnetic declination is the angle between the geographic meridian and the magnetic meridian. Magnetic dip is the angle the Earth's total magnetic field makes with the horizontal at a place.
• Q: What happens to a ferromagnetic material above its Curie temperature? A: Above its Curie temperature, a ferromagnetic material loses its ferromagnetic properties and behaves as a paramagnetic material.

Frequently Asked Questions