Magnetism and Matter – CBSE NCERT Study Resources

The hysteresis loop represents the lagging of magnetization (M) behind the magnetizing field (H) in ferromagnetic materials. It shows how the material retains some magnetization even after the external field is removed, known as remanence.

• Our textbook shows that the area of the loop indicates energy loss as heat during magnetization cycles.
• Materials like iron and cobalt exhibit large loops, making them suitable for permanent magnets.

In magnetic storage (e.g., hard disks), small loops are preferred for quick data rewriting, while large loops ensure data retention.

Research focuses on nanomaterials with tunable loops for high-density storage.

Earth's magnetic field arises from the dynamo effect, where convective currents in the liquid outer core generate electric currents, producing a magnetic field.

• Our textbook shows the field deflects solar winds, preventing atmospheric stripping.
• Paleomagnetic studies confirm field reversals over geological time.

Without this field, harmful cosmic rays would increase mutation rates, threatening life.

Monitoring field strength helps predict space weather hazards to satellites.

Materials respond differently to external fields: diamagnetic (weak repulsion), paramagnetic (weak attraction), and ferromagnetic (strong attraction).

• Diamagnetic: Bismuth repels fields (used in levitation experiments).
• Paramagnetic: Aluminum shows weak attraction in MRI machines.
• Ferromagnetic: Iron retains magnetization (used in transformers).

Ferromagnets dominate technology due to high permeability.

Graphene-based diamagnets may enable frictionless transport.

A moving coil galvanometer measures current via torque on a coil in a magnetic field, with deflection proportional to current.

• Our textbook shows a low-resistance shunt converts it into an ammeter.
• The shunt bypasses excess current, preserving coil sensitivity.

Without shunts, high currents would damage the delicate coil.

Digital ammeters now replace analog ones for precision.

Gauss's law for magnetism states that magnetic flux through a closed surface is zero, implying no magnetic monopoles exist.

• Our textbook shows experiments with bar magnets always produce dipoles.
• Quantum theories predict monopoles, but none are observed yet.

The law underpins Maxwell's equations, essential for electromagnetic theory.

Discovering monopoles could revolutionize particle physics.

The hysteresis loop represents the lag between magnetization (B) and magnetizing force (H) in ferromagnetic materials. Our textbook shows it is due to domain alignment resistance.

• Soft iron has a narrow loop (low coercivity), ideal for electromagnets.
• Steel has a wide loop (high coercivity), used for permanent magnets.

Energy loss (area under loop) is higher in steel, making it inefficient for AC applications. Soft iron’s rapid magnetization reversal minimizes energy dissipation.

Nanocrystalline alloys are emerging with tunable hysteresis, improving efficiency in transformers.

Magnetic susceptibility (χ) quantifies material response to external fields. We studied χ values: diamagnets (χ<0), paramagnets (χ>0), ferromagnets (χ≫0).

• Diamagnets: Bismuth (χ=−1.66×10⁻⁵) repels fields weakly.
• Paramagnets: Aluminum (χ=+2.2×10⁻⁵) aligns weakly with fields.
• Ferromagnets: Iron (χ~10³) retains magnetization.

Ferromagnets dominate technology (e.g., hard drives) due to high χ. Diamagnets enable MRI shielding.

Graphene-based diamagnets show potential for levitation technologies.

Torque (τ) on dipole moment (m) in field (B) is τ = m×B. Our textbook derives it from force pairs on pole strengths.

• Example 1: Moving coil galvanometer uses τ = NIABsinθ for current measurement.
• Example 2: Electric motors rely on τ to rotate armatures.

Maximum τ occurs at θ=90°. Precision instruments minimize frictional losses to enhance sensitivity.

MEMS-based micro-dipoles are enabling nanoscale actuators in medical devices.

Earth’s field (B) has: horizontal (H), vertical (V), and total (T) components. We studied B = √(H²+V²).

• At equator: V≈0, H≈30μT (IGRF 2020 data).
• At poles: H≈0, V≈60μT.

Compasses use H, which vanishes at magnetic poles. Satellite data shows 5% field strength decline since 1850.

Geomagnetic models predict pole reversal in ~2000 years, impacting navigation systems.

Magnetic susceptibility (χ) defines how materials respond to external fields. We studied χ values: diamagnetic (χ<0), paramagnetic (χ>0), ferromagnetic (χ≫0).

• Diamagnetic (e.g., Bismuth) weakly repel fields.
• Paramagnetic (e.g., Aluminum) weakly attract fields.
• Ferromagnetic (e.g., Iron) retain magnetization.

Ferromagnets dominate tech applications due to high χ. Diamagnets are used in MRI shielding.

Graphene-based diamagnets show promise for quantum levitation.

Earth acts as a giant dipole magnet with field lines from S to N geographic poles. [Diagram: Field lines deflecting solar winds].

• Magnetosphere deflects charged particles, preventing atmospheric stripping.
• Van Allen belts trap radiation, as per NCERT data.

Pole reversals (every 200k years) weaken protection temporarily.

Space missions study field decay (10% loss since 1800s) for risk assessment.

Magnetic domains are regions with aligned atomic dipoles. In unmagnetized iron, domains cancel out net magnetism.

• External fields align domains, creating net magnetization (Curie point: 770°C for iron).
• Domain walls move, shown in Barkhausen effect experiments.

Domain theory bridges atomic spin and bulk magnetic properties.

Single-domain nanoparticles could revolutionize high-density data storage.

The magnetic dipole moment (m) is a vector quantity that represents the strength and orientation of a magnetic dipole, such as a current-carrying loop. It is defined as the product of the current (I) flowing through the loop and the area vector (A) of the loop. Mathematically, it is expressed as:
m = I × A
where the direction of A is perpendicular to the plane of the loop, following the right-hand thumb rule.

To derive the expression for a circular loop of radius r:
1. Area of the loop, A = πr²
2. Magnetic dipole moment, m = I × πr²
The SI unit of m is Am² (ampere-meter squared).

Significance in torque: When a current-carrying loop is placed in a uniform magnetic field (B), it experiences a torque (τ) given by:
τ = m × B
This torque tends to align the magnetic dipole moment with the magnetic field, minimizing potential energy. The magnitude of torque is maximum when m and B are perpendicular and zero when they are parallel.

The Earth's magnetic field resembles that of a giant bar magnet with its south pole near the geographic north and vice versa. It has three key elements:
1. Magnetic Declination: The angle between the geographic meridian and magnetic meridian at a place.
2. Angle of Dip (δ): The angle between the Earth's magnetic field and the horizontal plane.
3. Horizontal Component (B_H): The component of Earth's field parallel to the surface.

A magnetic needle aligns itself along the resultant magnetic field of the Earth. In the absence of other influences:
1. The needle's north pole points towards the Earth's magnetic south.
2. It dips downward in the northern hemisphere and upward in the southern hemisphere due to the angle of dip.

The angle of dip varies with latitude:
- At the magnetic equator, δ = 0° (field is horizontal).
- At the magnetic poles, δ = 90° (field is vertical).
This alignment helps in navigation and compass applications.

The three types of magnetic materials differ in their response to an external magnetic field:

• Diamagnetic (e.g., Bismuth, Copper):
  - Weakly repelled by a magnetic field.
  - No permanent dipole moment; induced moment opposes the field.
  - Susceptibility (χ) is small and negative (~10^-5).
• Paramagnetic (e.g., Aluminum, Oxygen):
  - Weakly attracted by a magnetic field.
  - Has permanent dipoles that align with the field.
  - Susceptibility is small and positive (~10^-3 to 10^-5).
• Ferromagnetic (e.g., Iron, Nickel):
  - Strongly attracted by a magnetic field.
  - Permanent dipoles align in domains, creating a large net moment.
  - Susceptibility is large and positive (~10³ to 10⁵).

Behavior in a field:
- Diamagnets develop weak magnetization opposite to the field.
- Paramagnets align with the field but lose alignment when the field is removed.
- Ferromagnets retain alignment even after the field is removed (hysteresis).

The magnetic dipole moment (m) is a vector quantity that represents the strength and orientation of a magnetic dipole, such as a current-carrying loop or a bar magnet. It is defined as the product of the current (I) flowing through the loop and the area (A) enclosed by the loop, with its direction given by the right-hand thumb rule.

Derivation for a current-carrying loop:

Consider a circular loop of radius r carrying current I. The area of the loop is A = πr².

The magnetic dipole moment is given by: m = I × A.

Since the loop is circular, m = I × πr².

The direction of m is perpendicular to the plane of the loop, following the right-hand rule.

Significance:

• The torque (τ) experienced by the dipole in an external magnetic field B is given by τ = m × B, which determines its rotational behavior.
• The potential energy (U) of the dipole in the field is U = -m · B, indicating stable equilibrium when m aligns with B.
• It helps classify materials as diamagnetic, paramagnetic, or ferromagnetic based on their dipole moments.

The Earth's magnetic field resembles that of a giant bar magnet tilted at an angle to its rotational axis. Its key elements are:

• Magnetic Declination (θ): The angle between geographic north and magnetic north.
• Angle of Dip (δ): The angle between the Earth's magnetic field and the horizontal plane.
• Horizontal Component (B_H): The component of the field parallel to the surface.

Variation of Angle of Dip with Latitude:

• At the magnetic equator, the field is entirely horizontal (δ = 0°).
• As latitude increases, the angle of dip increases, reaching 90° at the magnetic poles.

Importance in Navigation:

• Compasses align with B_H, so accurate knowledge of δ ensures proper directional guidance.
• Pilots and sailors use dip circles to correct for deviations caused by δ at different latitudes.
• Helps in mapping and surveying by accounting for local magnetic anomalies.

The magnetic dipole moment (m) is a vector quantity that represents the strength and orientation of a magnetic dipole, such as a current-carrying loop. It is defined as the product of the current (I) flowing through the loop and the area vector (A) of the loop. The direction of the area vector is perpendicular to the plane of the loop, following the right-hand thumb rule.

For a circular loop of radius r carrying current I, the magnetic dipole moment is given by:
m = I × A
where A = πr² is the area of the loop. Thus, m = Iπr².

Significance:

• The torque (τ) experienced by the loop in a uniform magnetic field (B) is given by τ = m × B, which determines the rotational effect on the loop.
• The potential energy (U) of the loop in the magnetic field is U = -m · B, indicating stable equilibrium when m and B are aligned.

This concept is crucial in understanding the behavior of magnetic materials and devices like electric motors and MRI machines.

The Earth's magnetic field resembles that of a giant bar magnet tilted at an angle to its geographic axis. It has three main components:

• Magnetic Declination: The angle between the geographic meridian and magnetic meridian at a place.
• Magnetic Inclination (Dip): The angle made by the Earth's magnetic field with the horizontal.
• Horizontal Component (B_H): The component of Earth's magnetic field parallel to the surface.

A compass needle aligns itself with the magnetic meridian due to the torque exerted by Earth's magnetic field. The needle's magnetic dipole moment (m) experiences a torque τ = m × B, causing it to rotate until it aligns with B. The horizontal component (B_H) directs the needle north-south, while the vertical component influences its tilt.

Diagram (labeled):
[Earth's Magnetic Field Diagram]
1. Geographic North and South Poles
2. Magnetic North and South Poles
3. Magnetic field lines
4. Angle of Declination (θ)
5. Angle of Inclination (δ)

This alignment helps in navigation and studying Earth's geomagnetic properties.

The magnetic dipole moment (m) is a vector quantity that represents the strength and orientation of a magnetic dipole, such as a current-carrying loop or a bar magnet. It is defined as the product of the current (I) and the area (A) enclosed by the loop, with its direction given by the right-hand thumb rule.

For a circular loop of radius r carrying current I, the magnetic dipole moment is derived as follows:

Step 1: Area of the circular loop, A = πr².
Step 2: Magnetic dipole moment, m = I × A.
Step 3: Substituting the area, m = I × πr².

The direction of m is perpendicular to the plane of the loop, following the right-hand rule. The significance of magnetic dipole moment lies in its ability to determine the torque (τ) experienced by the dipole in an external magnetic field (B), given by τ = m × B. It also helps calculate the potential energy (U) of the dipole in the field, U = -m · B, which explains the alignment of dipoles along the field to minimize energy.

The hysteresis loop is a graphical representation of the relationship between the magnetizing force (H) and the magnetic flux density (B) in a ferromagnetic material. It shows how the material retains magnetization even after the external field is removed.

Key features of the hysteresis loop:

• Retentivity: The residual magnetization (B_r) when H is reduced to zero. It indicates the material's ability to retain magnetism.
• Coercivity: The reverse magnetizing force (H_c) required to reduce B to zero. It measures the resistance to demagnetization.

The loop is formed due to the lagging of B behind H, caused by domain alignment and energy losses. In transformers, a narrow hysteresis loop (low H_c and B_r) is preferred to minimize energy loss as heat (hysteresis loss). Materials like soft iron are used for efficient energy transfer.

The hysteresis loop is a graphical representation of the relationship between the magnetic field intensity (H) and the magnetic flux density (B) in a ferromagnetic material. It shows how the material retains magnetization even after the external field is removed, highlighting its retentivity and coercivity.

Key features of the hysteresis loop:

• Retentivity: The residual magnetization (B_r) when H is reduced to zero. It indicates the material's ability to retain magnetism.
• Coercivity: The reverse field (H_c) required to reduce B to zero. It measures the resistance to demagnetization.

Practical implications:

• Electromagnets: Soft ferromagnetic materials (narrow loop) are used due to low H_c, enabling easy magnetization and demagnetization.
• Permanent magnets: Hard ferromagnetic materials (wide loop) with high B_r and H_c retain magnetism for long periods.

The loop also illustrates energy loss as heat (hysteresis loss), which is minimized in transformers using soft iron cores.