JEE Mains Physics · Magnetism and Matter

Magnetic Properties of Materials and Hysteresis

A material placed in a field H becomes magnetised, M = χH, so the field inside rises to μ₀(H + M); the sign and size of χ sort materials into diamagnetic, paramagnetic and ferromagnetic, and a ferromagnet's hysteresis loop decides what it is used for.

All Magnetism and Matter notes JEE Mains Physics strategy

Why this matters

Twenty-three PYQs, half the chapter, three of them asking for a number and two from 2026. Ten test the three classes of material statement by statement, nine use the relations between H, χ and μ, and four ask why soft iron suits an electromagnet or what current demagnetises a magnet. Most are settled by one exact fact, so learn the table rather than the gist.

Concept 1 of 3: Magnetic intensity, susceptibility and permeability

The current in a solenoid sets the magnetic intensity H = ni, whatever fills the core. The core then magnetises itself, M = χH, and adds its own field, so B = μ₀(H + M). If χ is small the core changes B by the fraction χ; if it is large, as in iron, B grows hundreds of times. Permeability and susceptibility describe the same response and differ by one.

Definition

Magnetic intensity H, unit $A\,m^{-1}$ ; in a solenoid or toroid $H = ni$ .
Magnetisation $M = \chi H$ (moment per unit volume, $A\,m^{-1}$ ); χ has no unit.
$B = \mu_0(H + M) = \mu_0(1 + \chi)H = \mu H$ , with $\mu = \mu_0\mu_r$ and $\mu_r = 1 + \chi$ . So $\chi = \dfrac{\mu}{\mu_0} - 1$ .
Filling a solenoid or toroid with a material raises B by the fraction $\dfrac{B - B_0}{B_0} = \chi$ ; as a percentage, $100\chi$ .
The magnetic moment of a core of volume V: $m = MV = (\mu_r - 1)\,niV$ .
Units: B in tesla or gauss ( $1\ G = 10^{-4}\ T$ ); H in $A\,m^{-1}$ ; flux in weber; magnetic moment in $A\,m^{2}$ .

Magnetising a material

M = \chi H \qquad B = \mu_0(H + M) = \mu_0\mu_r H \qquad \mu_r = 1 + \chi \qquad \frac{\Delta B}{B_0} = \chi

Worked example

A long solenoid has 2000 turns per metre and carries 0.5 A. Its core has relative permeability 600. Find H, B and the magnetisation of the core.

(\mu_0 = 4\pi \times 10^{-7}\ T\,m\,A^{-1})

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

JEE Mains · 2023 · 11 April 2023 · Q13Moderate

Example 1 · Magnetism and Matter · Magnetic Properties of Materials and Hysteresis

The free space inside a current carrying toroid is filled with a material of susceptibility

2 \times10^{- 2}

. The percentage increase in the value of magnetic field inside the toroid will be

Fraction and percentage

Filling a solenoid raises B by the fraction χ. The percentage rise is 100χ. Options often offer both, one of them a hundred times off.

Relative permeability and susceptibility differ by one

μᵣ = 1 + χ. For a strongly magnetic material the difference hardly matters, but for a susceptibility near zero, using χ in place of μᵣ throws the answer away.

Drill 8 more on magnetic intensity, susceptibility and permeability

Concept 2 of 3: Diamagnetic, paramagnetic and ferromagnetic materials

In a diamagnet the atoms have no moment of their own; the field changes the electrons' orbits and induces a small moment opposite to it, so the material is weakly pushed out of a strong field. A paramagnet's atoms carry moments that the field lines up a little against thermal jostling, so it is weakly pulled in, and less so when hot. In a ferromagnet the moments line up by themselves in regions called domains, so the pull is strong, until heating past the Curie temperature breaks the domains apart.

Definition

Diamagnetic: $-1 \leq \chi < 0$ ; $\chi = -1$ is a perfect diamagnet (a superconductor). The induced moment opposes the field. Independent of temperature. Moves from a strong to a weak field.
Paramagnetic: χ small and positive. Curie's law $\chi = C/T$ . Moves from a weak to a strong field; only weakly attracted.
Ferromagnetic: χ very large. Each domain is magnetised to saturation; in an applied field, domains along the field grow and the others shrink and turn. Above the Curie temperature $T_C$ it becomes paramagnetic, with $\chi = C/(T - T_C)$ .
Graphs: M against H is a straight line of negative slope for a diamagnet and of positive slope for a paramagnet. χ against T is a flat negative line for a diamagnet and a falling curve for a paramagnet.

Property	Diamagnetic	Paramagnetic	Ferromagnetic
Susceptibility χ	Small, negative: −1 ≤ χ < 0	Small, positive	Very large, positive
Relative permeability μᵣ	Slightly less than 1	Slightly more than 1	Much greater than 1
Atomic moments	None; the field induces a moment opposite to itself	Permanent, randomly oriented without a field	Permanent, aligned within domains
In a non-uniform field	Moves from strong to weak field	Moves from weak to strong field, weakly attracted	Strongly attracted
Effect of temperature	χ does not depend on temperature	χ = C/T (Curie's law)	Paramagnetic above the Curie temperature
M against H	Straight line, negative slope	Straight line, small positive slope	Curved, saturates, shows hysteresis
Examples	Bismuth, copper, water, superconductors	Aluminium, sodium, oxygen	Iron, cobalt, nickel

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

JEE Mains · 2024 · 8 April 2024 · Q8Moderate

Example 2 · Magnetism and Matter · Magnetic Properties of Materials and Hysteresis

Paramagnetic substances: (A) align themselves along the directions of external magnetic field. (B) attract strongly towards external magnetic field. (C) has susceptibility little more than zero. (D) move from a region of strong magnetic field to weak magnetic field. Choose the most appropriate answer from the options given below:

Calling a strongly attracted material paramagnetic

Paramagnets are attracted only weakly. Strong attraction is the mark of a ferromagnet.

Getting the direction of drift backwards

A paramagnet moves from a weak field towards a strong one. A diamagnet moves the other way, from strong to weak.

Letting diamagnetism depend on temperature

Diamagnetism comes from moments induced in the electron orbits, not from aligning permanent moments, so heating does not change it. Only paramagnets and ferromagnets above the Curie point follow a temperature law.

Drill 9 more on diamagnetic, paramagnetic and ferromagnetic materials

Concept 3 of 3: Hysteresis and choosing a magnetic material

Take a ferromagnet round a cycle of H and its B lags behind, tracing a loop. When H is brought back to zero some magnetism stays: that is the retentivity. A reverse H is needed to remove it: that is the coercivity. An electromagnet must switch on and off with its current, so it wants a material that keeps little and lets go easily. A permanent magnet wants the opposite.

Definition

Retentivity (remanence): the B left when H returns to zero, where the loop cuts the B-axis.
Coercivity: the reverse H needed to bring B to zero, where the loop cuts the H-axis.
The area of the loop is the energy lost as heat in each cycle.
Electromagnet and transformer cores: soft iron, with high permeability, low retentivity and low coercivity.
Permanent magnets: steel or alnico, with high retentivity and high coercivity.
To demagnetise a magnet inside a solenoid, the solenoid's H must reach the coercivity: $H = ni$ , with $n = N/L$ .

Use	Material	Retentivity	Coercivity	Hysteresis loop
Electromagnet core	Soft iron	Low	Low	Narrow, small area
Transformer core	Soft iron, laminated	Low	Low	Narrow, so little energy is lost each cycle
Permanent magnet	Steel, alnico, cobalt steel	High	High	Wide, large area

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

JEE Mains · 2024 · 8 April 2024 · Q111Moderate

Example 3 · Magnetism and Matter · Magnetic Properties of Materials and Hysteresis

The coercivity of a magnet is

5 \times10^{3}\text{ }A/m

. The amount of current required to be passed in a solenoid of length

30\text{ }cm

and the number of turns 150, so that the magnet gets demagnetised when inside the solenoid is _____ A.

Swapping retentivity and coercivity

Retentivity is a value of B, read where the loop cuts the B-axis. Coercivity is a value of H, read where it cuts the H-axis.

Wanting a large retentivity in an electromagnet

An electromagnet must lose its magnetism when the current stops. Soft iron is chosen for its high permeability and its low retentivity and coercivity.

Drill 3 more on hysteresis and choosing a magnetic material

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (1)

Magnetic intensity, susceptibility and permeability
Magnetising a material
$M = \chi H \qquad B = \mu_0(H + M) = \mu_0\mu_r H \qquad \mu_r = 1 + \chi \qquad \frac{\Delta B}{B_0} = \chi$

Reference tables (2)

Diamagnetic, paramagnetic and ferromagnetic materials7 rows

Property	Diamagnetic	Paramagnetic	Ferromagnetic
Susceptibility χ	Small, negative: −1 ≤ χ < 0	Small, positive	Very large, positive
Relative permeability μᵣ	Slightly less than 1	Slightly more than 1	Much greater than 1
Atomic moments	None; the field induces a moment opposite to itself	Permanent, randomly oriented without a field	Permanent, aligned within domains
In a non-uniform field	Moves from strong to weak field	Moves from weak to strong field, weakly attracted	Strongly attracted
Effect of temperature	χ does not depend on temperature	χ = C/T (Curie's law)	Paramagnetic above the Curie temperature
M against H	Straight line, negative slope	Straight line, small positive slope	Curved, saturates, shows hysteresis
Examples	Bismuth, copper, water, superconductors	Aluminium, sodium, oxygen	Iron, cobalt, nickel

Hysteresis and choosing a magnetic material3 rows

Use	Material	Retentivity	Coercivity	Hysteresis loop
Electromagnet core	Soft iron	Low	Low	Narrow, small area
Transformer core	Soft iron, laminated	Low	Low	Narrow, so little energy is lost each cycle
Permanent magnet	Steel, alnico, cobalt steel	High	High	Wide, large area

Watch out for (7)

Fraction and percentage
→ Magnetic intensity, susceptibility and permeability
Relative permeability and susceptibility differ by one
→ Magnetic intensity, susceptibility and permeability
Calling a strongly attracted material paramagnetic
→ Diamagnetic, paramagnetic and ferromagnetic materials
Getting the direction of drift backwards
→ Diamagnetic, paramagnetic and ferromagnetic materials
Letting diamagnetism depend on temperature
→ Diamagnetic, paramagnetic and ferromagnetic materials
Swapping retentivity and coercivity
→ Hysteresis and choosing a magnetic material
Wanting a large retentivity in an electromagnet
→ Hysteresis and choosing a magnetic material

Test yourself on Magnetism and Matter

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