Class 12 Physics · NCERT chapter 5 · 7 topics · free to read
Bar Magnet
A bar magnet is the simplest magnetic dipole — it has a north pole and a south pole, creates a magnetic field pattern identical to a solenoid, and obeys Gauss's law for magnetism (net magnetic flux through any closed surface is zero).
B d A = 0
Bar Magnet Basics
A bar magnet always has a North pole and a South pole. Unlike electric charges, you can never isolate a single magnetic pole — breaking a magnet just gives you two smaller magnets.
A bar magnet has two ends called poles — the North-seeking pole (N) and the South-seeking pole (S). When freely suspended, the N-pole points roughly toward geographic north.
The most important fact: magnetic monopoles do not exist. If you break a bar magnet in half, you get two complete magnets, each with its own N and S pole. This is fundamentally different from electric charges, where you can isolate a positive charge from a negative charge.
Like poles repel, unlike poles attract — same rule as electric charges
Magnetic monopoles have never been found in nature (Dirac predicted them, but no experimental evidence yet)
The strength of a magnet is concentrated at the poles — the middle is the neutral zone
A freely suspended magnet aligns along the Earth's magnetic field (basis of a compass)
Quick recall
If you cut a bar magnet into 3 pieces, how many magnets do you get?
3 complete magnets — each with its own N and S pole. You can never isolate a single pole.
Magnetic Field Lines
Field lines are imaginary curves that map the direction and strength of the magnetic field. They form continuous closed loops — no starting or ending point.
Magnetic field lines emerge from the N-pole, travel through external space, enter the S-pole, and then continue inside the magnet from S to N. This forms continuous closed loops — they never start or end anywhere.
The tangent to a field line at any point gives the direction of B at that point. Where lines are crowded together, the field is strong; where they spread apart, the field is weak.
Start on +ve charge, end on −ve charge
Form continuous closed loops (no start/end)
Can begin/end at infinity
Always close on themselves
Isolated charges exist (monopoles)
No magnetic monopoles exist
E d A = q/ _0 (can be non-zero)
B d A = 0 (always zero)
Field lines never cross each other (if they did, B would have two directions at one point — impossible)
Outside the magnet: N → S direction; Inside the magnet: S → N direction
Density of field lines ∝ strength of B
At the axial point (on the axis far away), B 1/r^3 — same as electric dipole
Bar Magnet as a Solenoid
The magnetic field of a bar magnet looks exactly like that of a solenoid carrying current. NCERT establishes this analogy as a core concept.
A current-carrying solenoid produces a magnetic field pattern that is identical to a bar magnet at points far from the magnet/solenoid. The end where current flows counterclockwise (viewed from outside) acts as the N-pole.
m = NIA
The magnetic dipole moment m of a solenoid with N turns, current I , and cross-sectional area A is m = NIA . This is the same formula used for a bar magnet's dipole moment — reinforcing the equivalence.
At large distances, both bar magnet and solenoid behave as magnetic dipoles
The axial field at distance r (for r l ): B_ axial = _0 4 2m r^3
The equatorial field at distance r : B_ equatorial = _0 4 m r^3
B_ axial = 2 B_ equatorial at the same distance
Gauss's Law for Magnetism
The magnetic equivalent of Gauss's law in electrostatics, but with a twist: the total magnetic flux through any closed surface is always zero because magnetic monopoles don't exist.
B d A = 0
Gauss's law for magnetism states that the net magnetic flux through any closed surface is zero. This means every field line that enters a closed surface must also leave it — no field lines can 'originate' or 'terminate' inside.
This is one of Maxwell's four equations and is sometimes called the 'no-monopole law'. It applies to ALL magnetic fields — from bar magnets, solenoids, Earth's field, or any source.
Magnetic flux _B = B d A = 0 for any closed surface
This is equivalent to saying: magnetic field lines form closed loops
Contrast with Gauss's law for electricity where enclosed charge gives non-zero flux
This law holds even if a magnet is placed inside the surface — equal flux enters and exits
Quick recall
A bar magnet is enclosed completely inside a spherical surface. What is the net magnetic flux through the sphere?
Zero. By Gauss's law for magnetism, B d A = 0 always. Every field line that exits the sphere (from N-pole region) re-enters it (at S-pole region).
This is NCERT Section 5.2.3. The contrast between Gauss's law for E (can be non-zero) and for B (always zero) is a classic NEET comparison question.
Magnetic Dipole Moment
The magnetic dipole moment quantifies the strength and orientation of a magnetic source. For a current loop, m = NIA. A bar magnet and a current loop both behave as dipoles, experiencing torque and possessing potential energy in an external field.
m = NI A
Magnetic Dipole Moment
The magnetic dipole moment m tells you how strong a magnetic source is and which way it 'points'. It's the magnetic equivalent of the electric dipole moment p = qd.
The magnetic dipole moment m of a current loop is defined as m = NI A , where N = number of turns, I = current, and A = area vector (perpendicular to the loop, direction by right-hand rule).
m = NI A (SI unit: A·m^2 or J/T)
For a bar magnet, m points from the S-pole to the N-pole (inside the magnet). Its magnitude depends on the pole strength ( q_m ) and magnetic length ( 2l ): m = q_m 2l .
SI unit: A·m² (ampere-metre squared) or equivalently J/T (joule per tesla)
Direction: from S to N inside the magnet (or by right-hand rule for a current loop)
For a circular coil: m = NI( r^2) where r is the radius
m is a vector — both magnitude and direction matter in torque/energy calculations
Torque on a Magnetic Dipole
When placed in a uniform external magnetic field, a magnetic dipole experiences a torque that tries to align it with the field. This is why a compass needle rotates.
= m B = mB
The torque = mB is maximum when = 90° (dipole perpendicular to field) and zero when = 0° or 180° (dipole aligned or anti-aligned with field).
Torque is a cross product: = m B
_ = mB when = 90°
= 0 when = 0° (stable equilibrium) or = 180° (unstable equilibrium)
The torque tries to DECREASE — it's a restoring torque
Quick recall
A bar magnet with dipole moment m = 0.5 A·m² is placed at 30° to a field B = 0.2 T. What is the torque?
= mB = 0.5 0.2 30° = 0.5 0.2 0.5 = 0.05 N·m.
Potential Energy of a Dipole
A magnetic dipole in an external field has potential energy that depends on its orientation. Minimum energy at alignment, maximum at anti-alignment.
U = - m B = -mB
The potential energy U = -mB is minimum ( U = -mB ) when = 0° (aligned — stable equilibrium) and maximum ( U = +mB ) when = 180° (anti-aligned — unstable equilibrium).
= pE
= mB
U = -pE
U = -mB
Stable at = 0°
Stable at = 0°
= p E
= m B
The work done in rotating the dipole from angle _1 to _2 is: W = U( _2) - U( _1) = mB( _1 - _2) .
The magnetic field due to a dipole at far-away points depends on position: axial field is twice the equatorial field at the same distance.
B_ axial = _0 4 2m r^3 B_ equatorial = _0 4 m r^3
These formulas are valid for r l (far from the dipole). The axial field is along m and the equatorial field is anti-parallel to m . Both fall off as 1/r^3 — much faster than a monopole's 1/r^2 .
Axial point: on the axis of the magnet (extended N-S line)
Equatorial point: on the perpendicular bisector of the magnet
At axial point: B is parallel to m (same direction)
At equatorial point: B is anti-parallel to m (opposite direction)
Both fields 1/r^3 — dipole fields fall off faster than monopole fields
Quick recall
The magnetic field at an axial point at distance r from a short bar magnet is B . What is the field at an equatorial point at the same distance?
B/2 . Because B_ axial = 2 B_ equatorial at the same distance.
These formulas are identical in structure to the electric dipole formulas ( E_ axial = 1 4 _0 2p r^3 ), with p m and _0 1/ _0 . NCERT emphasizes this analogy in Table 5.1.
Earth's Magnetism
Earth behaves as a giant magnetic dipole tilted ~11.3° from its rotational axis. The three magnetic elements — declination, dip (inclination), and horizontal component — completely describe the Earth's magnetic field at any location.
B_H = B B_V = B
Earth as a Giant Magnet
Earth's interior generates a magnetic field that resembles a giant bar magnet tilted at about 11.3° to the rotational axis. This field shields us from deadly solar radiation.
Earth's magnetic field is produced by convection currents in the molten iron-nickel outer core (the dynamo theory). The field looks like that of a giant bar magnet placed at the center, tilted about 11.3° from the rotation axis.
The magnetic poles don't coincide with geographic poles. The magnetic south pole (near geographic north) is currently in northern Canada, about 1000 km from the geographic North Pole. It drifts by ~40 km per year.
Geographic North ≈ Magnetic South; Geographic South ≈ Magnetic North
Tilt angle between magnetic and geographic axes: ~ 11.3°
Earth's magnetic field strength: ~ 0.3 to 0.6 gauss ( 30 to 60 T)
The field protects Earth from solar wind — creating the magnetosphere
Magnetic poles drift over time — they're not fixed
Magnetic Elements
Declination (θ), dip/inclination (δ), and horizontal component (B_H) together completely specify the Earth's magnetic field vector at any location on Earth's surface.
At any point on Earth, the total magnetic field B is generally tilted — it's neither horizontal nor vertical. We describe it using three quantities called elements of Earth's magnetic field.
Declination ( ): Angle between geographic north and magnetic north (in the horizontal plane). It tells you how much your compass deviates from true north.
Dip / Inclination ( ): Angle between the total field B and the horizontal. At the equator, = 0° ; at the magnetic poles, = 90° .
Horizontal Component ( B_H ): The component of B along the horizontal direction. A compass needle responds to B_H , not the total B .
B_H = B B_V = B = B_V B_H
B = B_H^2 + B_V^2
At the magnetic equator: = 0° , so B_H = B and B_V = 0 (the field is entirely horizontal). At the magnetic poles: = 90° , so B_V = B and B_H = 0 (the field is entirely vertical — a compass is useless here!).
Quick recall
At a place where = 60° and B = 0.4 gauss, what is B_H ?
B_H = B 60° = 0.4 0.5 = 0.2 gauss.
Declination & Dip in Practice
Declination and dip vary with geographic location. Understanding their variation helps predict compass behavior at different latitudes.
Declination varies from place to place and even changes slowly over time. In India, declination is relatively small (about 0° to 2° E). In some parts of the world, it can be as large as 20° .
Dip varies systematically with latitude: 0° at the magnetic equator (field is horizontal) and 90° at the magnetic poles (field is vertical). An isogonic line connects places with equal declination; an isoclinic line connects places with equal dip.
Magnetic equator: = 0° , B_H = B (compass works perfectly)
Magnetic poles: = 90° , B_H = 0 (compass is useless)
India lies between ~ 0° to ~ 45° dip; declination is small
Quick recall
Where on Earth is the angle of dip exactly 0°?
At the magnetic equator (also called the aclinic line). Here the Earth's field is perfectly horizontal.
NCERT Section 5.3 discusses the elements of Earth's magnetic field. Most NEET problems involve the triangle relations between B , B_H , B_V , and — practice these numerical problems.
Magnetization & Magnetic Intensity
Magnetization M measures how much a material is magnetized per unit volume. Magnetic intensity H is the external 'driving' field. The total field inside a material is B = μ₀(H + M), connecting the external cause (H) to the material's response (M).
B = _0( H + M )
Magnetization (M)
Magnetization M is the net magnetic dipole moment per unit volume of a material. It tells you how much the material contributes to the total magnetic field.
When a material is placed in an external magnetic field, its atomic dipoles tend to align (partially or fully). Magnetization M quantifies this alignment as the net magnetic moment per unit volume.
M = Net magnetic dipole moment Volume = m _i V (unit: A/m)
SI unit of M : A/m (ampere per metre)
For unmagnetized material: M = 0 (atomic moments cancel out due to random orientation)
For fully magnetized material: M = M_ sat (all dipoles aligned — saturation)
M is a macroscopic quantity — it averages over billions of atomic dipoles
Magnetic Intensity (H)
H represents the magnetic field component due to external sources (like current in a solenoid) alone, ignoring the material's own contribution. It's the 'cause' that produces magnetization.
Magnetic intensity (or magnetizing field) H represents the external influence that magnetizes a material. For a solenoid with n turns per unit length carrying current I : H = nI .
H = nI (for a solenoid) SI unit: A/m
H depends only on the external source (current, geometry) and NOT on the material inside. It's the same whether the solenoid core is air, iron, or vacuum. The material responds to H by developing magnetization M .
SI unit of H : A/m (same as M )
H is independent of the material — it depends only on free currents
H is sometimes called the auxiliary magnetic field or magnetizing field
In vacuum: M = 0 , so B = _0 H
The Master Relation: B = μ₀(H + M)
The total magnetic field B inside a material is the sum of the external contribution (μ₀H) and the material's own contribution (μ₀M). This single equation unifies all of magnetic material behavior.
B = _0( H + M )
This is the fundamental equation of magnetism in materials. _0 H is what the field would be without the material (vacuum contribution). _0 M is the extra field the material adds due to its magnetization.
In vacuum: M = 0 , so B = _0 H
In a material: B = _0(H + M) — material contribution adds (or subtracts) from the external field
_0 = 4 10^ -7 T·m/A (permeability of free space)
Magnetic Susceptibility & Permeability
Susceptibility (χ) tells you how strongly a material magnetizes in response to H. Permeability (μ) tells you the total B produced per unit H. These are the key classifiers for magnetic materials.
Magnetic susceptibility (chi) is the ratio of magnetization to magnetic intensity. It tells you how 'responsive' a material is to an applied magnetic field.
= M H (dimensionless)
Substituting M = H into B = _0(H + M) : B = _0 H(1 + ) = _0 _r H = H , where _r = 1 + is the relative permeability and = _0 _r is the absolute permeability.
B = _0(1 + )H = _r _0 H = H
_r = 1 + = _0 _r
< 0 → Diamagnetic
_r < 1 → Diamagnetic
> 0 (small) → Paramagnetic
_r > 1 (slightly) → Paramagnetic
>> 1 (very large) → Ferromagnetic
_r >> 1 (very large) → Ferromagnetic
Dimensionless ratio M/H
Dimensionless ratio B/( _0 H)
_r = 1 +
= _r - 1
is dimensionless (no units) — it's a ratio of two quantities with the same unit (A/m)
Diamagnetic: < 0 (material opposes the field)
Paramagnetic: > 0 but small (~ 10^ -5 to 10^ -3 )
Ferromagnetic: >> 1 (can be 10^3 to 10^5 )
_r = 1 for vacuum; _r < 1 for diamagnetic; _r >> 1 for ferromagnetic
Diamagnetic Materials
Diamagnetic materials have no permanent magnetic dipoles. When placed in an external field, they develop a weak magnetization OPPOSITE to the field (χ < 0). Examples: bismuth, copper, diamond, water. Superconductors are perfect diamagnets (χ = −1).
< 0 (typically -10^ -5 )
Diamagnetic Mechanism
Diamagnetism arises because an external magnetic field slightly modifies the orbital motion of electrons, inducing a tiny magnetic moment that opposes the applied field. It's present in ALL materials but usually masked by stronger effects.
In diamagnetic materials, atoms have no net permanent magnetic moment (all electron spins and orbital moments cancel). When you apply an external field B , it slightly changes the electron orbital speeds, inducing a tiny moment that opposes B .
This is actually a consequence of Lenz's law at the atomic level: changing flux through electron orbits induces currents that oppose the change. The induced moment always opposes the applied field, regardless of the field's direction.
Atoms have zero permanent dipole moment (all moments cancel in pairs)
External field induces a weak opposing moment (Lenz's law at atomic level)
< 0 (typically -10^ -5 ) — negative because M opposes H
Effect is universal — ALL materials show diamagnetism, but in para/ferro materials, stronger effects dominate
Diamagnetism is independent of temperature (it's an orbital effect, not thermal)
Properties & Examples
Diamagnetic materials are weakly repelled by magnets, have slightly reduced internal fields, and are the only type of magnetism that is temperature-independent.
When a diamagnetic rod is placed in a non-uniform field, it moves from stronger to weaker field regions (it's repelled). In a uniform field, the field lines are slightly less dense inside the material than outside.
_r < 1 (slightly less than 1) — so B inside is slightly less than _0 H
In non-uniform field: material moves toward weaker field (repelled from strong field)
Temperature has no effect on diamagnetic susceptibility
Superconductors
Superconductors exhibit perfect diamagnetism (χ = −1): they completely expel all magnetic flux from their interior. This is called the Meissner effect.
Below a critical temperature T_c , certain materials become superconductors — zero electrical resistance AND perfect diamagnetism. They expel ALL magnetic flux from their interior: B_ inside = 0 .
= -1 _r = 0 B_ inside = 0
This perfect flux expulsion is called the Meissner effect. While ordinary diamagnets reduce B by a tiny amount ( -10^ -5 ), superconductors reduce it to exactly zero ( = -1 ).
= -1 exactly — the most extreme possible diamagnetic response
_r = 1 + = 0 — permeability is zero
B = _0(H + M) = 0 M = -H — magnetization exactly cancels the applied field
Only works below the critical temperature T_c (e.g., T_c = 7.2 K for lead)
NCERT mentions this as a 'limiting case' of diamagnetism
Quick recall
For a superconductor in a magnetic field, what is the value of _r ?
_r = 0 . Since = -1 , we get _r = 1 + (-1) = 0 , meaning the material allows zero magnetic field inside.
NCERT Section 5.4.1 introduces the Meissner effect. While NEET rarely asks deep questions about superconductivity, knowing = -1 and the Meissner effect name is enough for any MCQ on this topic.
Paramagnetic & Ferromagnetic Materials
Paramagnetic materials have permanent atomic dipoles that weakly align with the external field (χ > 0, small). Ferromagnetic materials have domains of aligned dipoles that produce strong magnetization (χ >> 1). Curie's law and Curie temperature govern their temperature dependence.
= C T (Curie's Law for paramagnets)
Paramagnetic Materials
Paramagnetic materials have permanent atomic dipoles that tend to align with an external field, but thermal agitation keeps them mostly random. The net alignment is weak and proportional to B/T.
In paramagnetic materials, each atom has a permanent magnetic dipole moment (due to unpaired electrons). Without an external field, thermal energy keeps these moments randomly oriented — so M = 0 .
Apply an external field B , and the dipoles partially align along B . The alignment competes with thermal randomization. Result: a weak, positive magnetization in the direction of the applied field.
Atoms have permanent dipole moments (unlike diamagnets which have none)
> 0 but small ( 10^ -5 to 10^ -3 ) — weakly attracted to magnets
In non-uniform field: material moves toward stronger field region
Field lines are slightly more dense inside than outside
For paramagnetic materials, susceptibility is inversely proportional to absolute temperature. Higher temperature → more thermal randomization → weaker alignment → lower χ.
= C T
Curie's law states that paramagnetic susceptibility is inversely proportional to the absolute temperature T (in Kelvin). C is the Curie constant, which depends on the material.
Physical meaning: at high temperatures, thermal energy is large, so atomic dipoles stay mostly random despite the field — is small. At low temperatures, thermal randomization is weak, dipoles align better — is large.
Curie's law: = C/T (valid only for paramagnets, not diamagnets or ferromagnets)
As T : 0 (paramagnet becomes effectively non-magnetic)
As T 0 : (in practice, the material may become ferromagnetic before this)
C is material-specific and does not depend on temperature
Diamagnetic does NOT follow Curie's law — it's temperature-independent
Quick recall
A paramagnetic material has = 3 10^ -4 at 300 K. What is at 600 K?
By Curie's law, 1/T . Doubling T halves . So = 1.5 10^ -4 at 600 K.
Ferromagnetic Materials
Ferromagnetic materials exhibit extremely strong magnetization due to a quantum mechanical exchange interaction that aligns neighboring atomic dipoles in large regions called domains.
Ferromagnetic materials show the strongest magnetic behavior in nature. Like paramagnets, their atoms have permanent dipoles. But here, a quantum mechanical exchange interaction strongly couples neighboring dipoles, forcing them to align parallel.
This creates large regions (~ 0.1 to 1 mm) called domains, where all atomic moments point in the same direction. In an unmagnetized state, different domains point in random directions, so the net M = 0 .
Examples: Iron (Fe), Cobalt (Co), Nickel (Ni), Gadolinium (Gd), and their alloys
>> 1 (typically 10^3 to 10^5 ) — very strong attraction to magnets
_r >> 1 — field inside is much stronger than the applied field
Domain structure — large regions of aligned dipoles
Applying a field: favorable domains grow, unfavorable domains shrink → net M appears
Ferromagnets can retain magnetization after the field is removed (permanent magnets!)
Curie Temperature
Above the Curie temperature T_C, thermal energy destroys the exchange coupling, and the ferromagnet becomes a paramagnet. Below T_C, domain structure and strong magnetization exist.
Every ferromagnetic material has a characteristic Curie temperature T_C above which it loses its ferromagnetic property and becomes paramagnetic. The thermal energy overcomes the exchange interaction.
= C T - T_C (Curie-Weiss law, for T > T_C)
Above T_C , the susceptibility follows the Curie-Weiss law: = C/(T - T_C) , which reduces to Curie's law ( = C/T ) when T >> T_C . At T = T_C , diverges — a phase transition occurs.
Curie temperature of Iron: T_C = 1043 K ( 770° C)
Curie temperature of Nickel: T_C = 631 K ( 358° C)
Curie temperature of Cobalt: T_C = 1394 K ( 1121° C)
Above T_C : paramagnetic (random dipoles, weak , no hysteresis)
Ferromagnetic
Paramagnetic
Domain structure exists
No domains — random dipole orientations
>> 1
small and positive
Hysteresis observed
No hysteresis
Retains magnetization
Loses all magnetization when field removed
Quick recall
What happens to a ferromagnetic material when heated above its Curie temperature?
It becomes paramagnetic — domains break up, strong magnetization disappears, and drops from ~ 10^4 to ~ 10^ -3 . It follows Curie-Weiss law: = C/(T - T_C) .
NCERT Table 5.3 lists the Curie temperatures. NEET sometimes asks: 'Above what temperature does iron become paramagnetic?' → 1043 K (or 770°C). Memorize the big three: Fe (1043 K), Co (1394 K), Ni (631 K).
Hysteresis
The hysteresis curve (B-H loop) shows how magnetization of a ferromagnet lags behind the applied field. Key quantities: retentivity (B at H=0), coercivity (H needed to demagnetize). The area of the loop represents energy lost per cycle as heat.
Energy loss per cycle = B dH (area of B-H loop)
The B-H Curve
When you cycle a ferromagnet through an alternating magnetic field, the B-H graph traces a closed loop. The magnetization doesn't retrace its path — it 'remembers' its history. This lag is called hysteresis.
Start with an unmagnetized ferromagnet ( B = 0, H = 0 ). Increase H : B increases rapidly as domains align, then saturates when all domains are aligned. Now decrease H back to zero: B does NOT return to zero — some magnetization remains.
The word hysteresis comes from Greek meaning 'lagging behind'. The magnetization B always lags behind the applied field H — it has a memory of its past state.
Saturation: Maximum B — all domains aligned, further increase in H doesn't increase B much
The loop is traversed in the direction: O → saturation → retentivity → coercivity → reverse saturation → back
The curve is NOT reversible — B at a given H depends on the history (whether H was increasing or decreasing)
Each complete cycle of the loop represents one full magnetization-demagnetization cycle
Retentivity & Coercivity
Retentivity is how much magnetization remains when the field is removed. Coercivity is how much reverse field is needed to completely demagnetize. Together they classify magnets as 'hard' or 'soft'.
Retentivity (or remanence) B_r : The value of B when H is reduced to zero after saturation. It's the magnetization the material 'retains' — the reason permanent magnets exist.
Coercivity H_c : The reverse magnetic intensity needed to bring B back to zero. It measures how 'stubbornly' the material holds on to its magnetization.
B_r = B |_ H=0 (retentivity) H_c = H |_ B=0 (coercivity)
High retentivity + High coercivity → good for permanent magnets (hard to demagnetize)
High retentivity + Low coercivity → good for electromagnets (easy to magnetize and demagnetize)
Retentivity B_r is measured in Tesla (T)
Coercivity H_c is measured in A/m
Both are read directly from the hysteresis curve: B_r on the B -axis, H_c on the H -axis
Quick recall
A material has high retentivity and high coercivity. Is it suitable for a permanent magnet or an electromagnet core?
Permanent magnet. High retentivity means it stays strongly magnetized. High coercivity means external fields can't easily demagnetize it. Both are desirable for permanent magnets.
Permanent Magnets vs Soft Magnets
The shape of the hysteresis loop determines whether a ferromagnetic material is suitable as a permanent magnet (wide loop) or as a transformer/electromagnet core (narrow loop).
High retentivity ( B_r )
Moderate retentivity
High coercivity ( H_c )
Low coercivity ( H_c )
Wide hysteresis loop (large area)
Narrow hysteresis loop (small area)
Hard to magnetize, hard to demagnetize
Easy to magnetize, easy to demagnetize
Examples: Steel, Alnico, Nd₂Fe₁₄B (neodymium)
Examples: Soft iron, Silicon steel, Mu-metal
Used in: speakers, fridge magnets, motors
Used in: transformer cores, electromagnets, relays
The area of the hysteresis loop equals the energy dissipated as heat per unit volume per cycle. For transformer cores (which undergo thousands of cycles per second at 50 Hz), you want the smallest possible loop to minimize energy waste.
Electromagnet cores: narrow loop (low H_c ) — easy demagnetization, low energy loss
Energy loss per cycle = area of hysteresis loop
Transformers need narrow-loop materials to minimize heating (I²R-like magnetic losses)
Neodymium magnets (Nd₂Fe₁₄B) are the strongest permanent magnets commercially available
Energy Loss in Hysteresis
Every time a ferromagnet goes through a complete magnetization cycle, energy equal to the area of the B-H loop is lost as heat. This is a crucial consideration in AC devices.
Energy loss per unit volume per cycle = B dH = Area of B-H loop
The energy lost per cycle is not wasted in creating magnetization — it goes into heating the material. This is called hysteresis loss. In devices operating at frequency f , the power loss is: P = f (loop area) (volume) .
Hysteresis loss = area of B-H loop (per unit volume, per cycle)
Power loss = (loop area) × (volume) × (frequency)
At 50 Hz AC, transformer cores cycle 50 times per second — narrow loops are essential
Hard magnets: large loop area → NOT suitable for AC applications
Soft magnets: small loop area → ideal for transformers, motors, generators
Quick recall
Why is soft iron preferred over steel for transformer cores?
Soft iron has a narrow hysteresis loop (small area = low energy loss per cycle) and low coercivity (easy to demagnetize). Steel has a wide loop — too much energy wasted as heat in every cycle at 50 Hz.
NCERT Section 5.6 covers permanent magnets and electromagnets. This is a frequently tested area — expect at least one MCQ on 'suitable material for permanent magnet / transformer core' in NEET.