Magnetism and Matter Class 12 Notes | YoLearn.ai

Fundamental Concepts of Magnetism

Magnetism, like electricity, is a fundamental force. A bar magnet has two poles, North (N) and South (S), which always exist in pairs; magnetic monopoles are hypothetical and have never been observed. The force between like poles is repulsive, and between unlike poles is attractive. The region around a magnet where its influence can be felt is called a magnetic field. This field is visualized using magnetic field lines, which originate from the North pole and terminate at the South pole outside the magnet, forming continuous closed loops. They never intersect each other, and their density indicates the strength of the magnetic field.

Every magnet possesses a magnetic dipole moment (M), a vector quantity directed from the South pole to the North pole. For a bar magnet, M = m 2l, where m is the pole strength and 2l is the magnetic length. For a current loop, M = NIA, where N is the number of turns, I is the current, and A is the area of the loop. When a magnetic dipole is placed in a uniform external magnetic field (B), it experiences a torque (τ) given by τ = M × B. The magnitude of this torque is τ = MB sinθ, where θ is the angle between M and B. The potential energy (U) of the dipole in the field is U = -M ⋅ B = -MB cosθ. A bar magnet can be considered an equivalent solenoid; its magnetic field on the axial line is B_axial = (μ₀/4π) (2M/r³) and on the equatorial line is B_equatorial = (μ₀/4π) * (M/r³) for r >> 2l. Gauss's Law for Magnetism states that the net magnetic flux through any closed surface is zero, ∮ B ⋅ dA = 0, reinforcing the non-existence of magnetic monopoles.

Earth's Magnetism and Magnetic Elements

Classification of Magnetic Materials

Key Definitions in Magnetism

Magnetic Intensity (H)

The ability of a magnetic field to magnetize a material. It represents the magnetizing field or magnetic field strength. H = B_ext / μ₀ in vacuum, or H = B/μ - M inside a material. SI unit: A/m.

Intensity of Magnetization (M)

The magnetic dipole moment per unit volume of a material. It indicates how much a material is magnetized when placed in an external magnetic field. M = m_net / V. SI unit: A/m.

Magnetic Susceptibility (χm)

A dimensionless quantity that describes how susceptible a material is to becoming magnetized in an applied magnetic field. It's the ratio of the intensity of magnetization (M) to the magnetic intensity (H): χm = M/H.

Relative Magnetic Permeability (μr)

The ratio of the magnetic permeability of a material (μ) to the permeability of free space (μ₀). It indicates how easily magnetic field lines can pass through a material. μr = μ/μ₀ = 1 + χm.

Curie Temperature (T_C)

The critical temperature above which a ferromagnetic material loses its ferromagnetism and becomes paramagnetic. Above T_C, thermal agitation overcomes the alignment of magnetic domains.

Retentivity (Remanence)

The ability of a material to retain its magnetism after the external magnetizing field has been removed. It is the value of residual magnetism at H=0 in a hysteresis loop.

Coercivity (Coercive Force)

The intensity of the reverse magnetizing field required to demagnetize a material completely (i.e., to reduce its residual magnetism to zero). It's a measure of the material's resistance to demagnetization.

Key Formulas and Must-Remember Relations

• Magnetic Dipole Moment (current loop): M = NIA (N: turns, I: current, A: area)
• Torque on a magnetic dipole in uniform field: τ = M × B (magnitude τ = MB sinθ)
• Potential Energy of a magnetic dipole: U = -M ⋅ B = -MB cosθ
• Gauss's Law for Magnetism: ∮ B ⋅ dA = 0 (implies no magnetic monopoles)
• Magnetic field in material: B = μ₀(H + M)
• Relation between permeability and susceptibility: μ = μ₀(1 + χm) and μr = 1 + χm
• Earth's magnetic elements: B_H = B_E cos δ, B_V = B_E sin δ, tan δ = B_V / B_H, B_E² = B_H² + B_V²
• Curie's Law (for Paramagnetic materials): χm ∝ 1/T

Worked Examples

• A bar magnet of magnetic moment 1.5 J/T is aligned with a uniform magnetic field of 0.22 T. What is the work required to turn the magnet so as to align its magnetic moment opposite to the field? Initial potential energy U_i = -MB cos 0° = -MB. Final potential energy U_f = -MB cos 180° = +MB. Work done W = U_f - U_i = MB - (-MB) = 2MB. Substituting values: W = 2 1.5 J/T 0.22 T = 0.66 J.
• At a certain location, the horizontal component of Earth's magnetic field is 0.3 G and the dip angle is 30°. What is the total magnetic field of the Earth at this location? (1 G = 10⁻⁴ T) We know B_H = B_E cos δ. Therefore, B_E = B_H / cos δ. B_E = 0.3 G / cos 30° = 0.3 G / (√3/2) = 0.6 / √3 G. B_E ≈ 0.346 G or 3.46 × 10⁻⁵ T.

Exam Traps & Marking Cues

1. Distinguish Electric vs. Magnetic Dipoles: Remember that electric field lines originate and terminate on charges, while magnetic field lines form closed loops because monopoles don't exist. This is a common conceptual trap.
2. Units: Always pay attention to units. Magnetic field can be given in Tesla (T) or Gauss (G), where 1 T = 10⁴ G. Magnetic moment is in A m² or J/T.
3. Properties of Magnetic Materials: Do not just list properties; understand why they behave that way (e.g., paired/unpaired electrons, domain formation). This helps in application-based questions. Be precise about the sign and magnitude of χm and μr for each material type.
4. Earth's Magnetic Elements: Clearly define and differentiate between magnetic declination and magnetic dip. Remember the conditions for zero dip angle (magnetic equator) and 90° dip angle (magnetic poles).

Practice Questions with Solutions

• Q: State two properties of magnetic field lines. A: They form continuous closed loops and never intersect each other.
• Q: What is the significance of Gauss's Law in magnetism? A: It implies that isolated magnetic poles (monopoles) do not exist, and magnetic field lines always form closed loops.
• Q: How does the magnetic susceptibility of a paramagnetic material change with temperature? A: It decreases with an increase in temperature, following Curie's Law (χm ∝ 1/T).
• Q: What is the direction of the magnetic dipole moment for a current loop? A: Its direction is given by the right-hand thumb rule, perpendicular to the plane of the loop.

Frequently Asked Questions