Brief Introduction to Magnetic Materials

Overview

This lecture covers the Magnetic Materials chapter for Maharashtra HSC 12th Board. It is a short chapter with 2-3 mark questions and involves the study of different types of magnetic materials (diamagnetic, paramagnetic, ferromagnetic), the origin of magnetism, and their properties.

Introduction to Magnetic Dipole Moment

• A bar magnet has a magnetic dipole moment, denoted by μ or m.
• Similar to electric dipole moment (P = 2QL), there is also a magnetic dipole moment.
• This is a characteristic feature of the magnet that represents its magnetic property.
• When a bar magnet is suspended, it aligns itself with the geographic north-south direction.
• This chapter deals in detail with various magnetic materials.

Torque on Magnetic Dipole in a Uniform Magnetic Field

• When a magnetic dipole is placed in a uniform magnetic field B, a torque acts on it.
• Torque formula: τ = M × B = MB sin θ (vector cross product).
• Here M = magnetic dipole moment, B = magnetic field, θ = angle between them.
• This formula is similar to P × E in an electric field.
• μ can also be used instead of M.

Magnetic Potential Energy

• Magnetic potential energy formula: U = -MB cos θ.
• In vector form: U = -M⃗ · B⃗ (dot product).
• This is analogous to U = -P⃗ · E⃗ in electrostatics.

Potential Energy in Different Situations:

• When M and B are parallel (θ = 0°): minimum energy and most stable state.
• When perpendicular (θ = 90°): potential energy is zero.
• When anti-parallel (θ = 180°): maximum energy and most unstable state.

Angular Oscillation and Time Period

• When a bar magnet is displaced in an external field and released, it undergoes oscillatory motion.
• Torque equation: τ = I d²θ/dt² (where I = moment of inertia).
• Restoring torque: τ = -MB sin θ.
• For small angles sin θ ≈ θ, resulting in: d²θ/dt² = -(MB/I)θ.
• This is the characteristic equation of SHM.
• Time period formula: T = 2π√(I/MB).

Origin of Magnetism

• The origin of magnetism lies in circulating electrons inside the atom.
• An electron revolving around the nucleus behaves like a current-carrying loop.
• The magnetic dipole moment of a current loop is: m = I × A.
• Therefore, every atom has a magnetic dipole moment.
• Due to paired and unpaired electrons, some materials exhibit magnetic properties while others do not.

Electron's Orbital Magnetic Moment

• When an electron revolves in a circular path around the nucleus, it forms a current loop.
• Magnetic moment of the current loop: m = IA (where I = current, A = area).
• Current: I = e/T = eω/2π.
• Area = πr² (for circular loop).
• Final formula: M_orbital = eVr/2 (where e = electron charge, V = velocity, r = radius).
• This formula is a 5-star topic and is frequently asked in exams.

Magnetization (M) and Magnetic Intensity (H)

• Magnetization (M) = magnetic dipole moment per unit volume = m_net/V.
• It is a vector quantity, unit: Ampere per meter (A/m).
• Magnetic intensity (H) = N × I (where N = turns per unit length, I = current).
• When a magnetic material is placed inside a solenoid: B = B₀ + B_m.
• B₀ = μ₀NI (field of solenoid), B_m = μ₀M (field of material).
• Total field: B = μ₀(H + M).
• From this: H = B/μ₀ - M.

Magnetic Susceptibility and Permeability

• Relation between magnetization and intensity: M = χH (where χ = magnetic susceptibility).
• Susceptibility indicates how much a material can be magnetized.
• B = μ₀(1 + χ)H = μ₀μ_r H.
• Relative permeability: μ_r = 1 + χ (this is a very important formula).
• Permeability (μ₀) indicates how much magnetic field a material allows inside it.
• Permittivity (ε₀) is a similar concept for electric fields.

Types of Magnetic Materials

Diamagnetic Materials

• Magnetic field lines pass through them minimally.
• They reduce the external magnetic field.
• Electron orbits are completely filled, net magnetic moment = 0.
• Align perpendicular to the magnetic field.
• Liquids placed in magnetic fields move towards the weaker part.

Paramagnetic Materials

• Have incomplete electron orbits (unpaired electrons).
• Magnetic dipoles are randomly oriented, net moment = 0 due to thermal agitation.
• Align parallel in an external field.
• Move from weaker to stronger part.
• Maximum field lines pass through.

Ferromagnetic Materials

• Explained by domain theory.
• Domains are small regions containing thousands to millions of dipoles aligned in the same direction.
• Without field, domains are randomly oriented; net moment = 0.
• In an external field, all domains align in one direction.
• Neighboring dipoles align due to exchange coupling.
• Domain size is a fraction of a millimeter, containing 10¹⁰ to 10¹⁷ atoms.
• The boundary between adjacent domains is called domain wall.

Effect of Temperature

• Heating ferromagnetic substances decreases susceptibility.
• At a particular temperature, the domain structure is destroyed.
• This temperature is called Curie temperature.
• Above Curie temperature, ferromagnetic materials behave like paramagnetic.
• Susceptibility of paramagnetic substances is positive but low.
• Increasing temperature also reduces paramagnetic susceptibility.
• Diamagnetic susceptibility is negative and independent of temperature.

Hysteresis Loop

• It is the graph between magnetic field (B) and magnetizing force (H).
• Initially, increasing H increases B until a saturation point is reached.
• Decreasing H does not bring B back to zero; some field is retained.
• Retentivity = the remaining B when H = 0.
• Coercivity = the opposite H required to reduce B to zero.
• Increasing H in the negative direction produces opposite saturation.
• Returning H to positive direction forms a complete loop.
• This cycle repeats continuously.

Permanent Magnet and Electromagnet

• Permanent Magnet: made from steel or hard magnetic materials, having high retentivity and coercivity.
• Electromagnet: made from soft iron (high permeability, low retentivity).
• Magnetization in electromagnets can be turned on/off by switching current.
• Electromagnets are used in electric bells, loudspeakers, circuit breakers.
• Soft iron magnetizes and demagnetizes quickly.
• Magnetization in permanent magnets lasts for a long time.

Magnetic Shielding

• When a hollow sphere/shell is placed in a magnetic field, the field lines pass through the solid material portion.
• No field lines enter the hollow portion.
• This hollow part is a shielded area where magnetic field does not reach.
• This principle is called magnetic shielding.
• Field lines concentrate in paramagnetic or ferromagnetic materials.
• This technique is used to protect sensitive equipment from magnetic fields.

Important Formulas

• Torque: τ = MB sin θ
• Potential energy: U = -MB cos θ
• Time period: T = 2π√(I/MB)
• Orbital magnetic moment: M = eVr/2
• Magnetization: M = m_net/V = χH
• Magnetic field: B = μ₀(H + M) = μ₀μ_r H
• Relative permeability: μ_r = 1 + χ
• Magnetic intensity: H = B/μ₀ - M