Magnetism and Matter

Magnetism is one of the most fascinating branches of physics, dealing with the interaction of materials with magnetic fields. Matter around us responds differently to a magnetic field depending on its internal structure and alignment of atomic dipoles.

The study of Magnetism and Matter explains:

• Why some materials are strongly attracted to magnets,
• Why some repel them,
• Why Earth itself behaves like a giant magnet.

1.0What is Magnetism?

Magnetism is a fundamental physical phenomenon that arises due to the motion of electric charges. Every electron in an atom has two kinds of motion — orbital motion around the nucleus and spin motion around its own axis. These motions create tiny magnetic dipoles.

• When these dipoles cancel each other $\to$ the material shows no net magnetism.
• When dipoles align in a particular direction $\to$ the material exhibits magnetism.

Magnetism Examples:

• Iron nails stick to a bar magnet because iron is ferromagnetic.
• A compass needle aligns itself with Earth’s magnetic field because Earth itself behaves like a giant magnet.

2.0Types of Magnetism

Different materials respond differently when placed in a magnetic field. Based on their behavior, magnetism is classified into three main types:

1. Diamagnetism

• Property: Weakly repelled by an external magnetic field.
• Cause: Induced magnetic dipoles oppose the applied field.
• Susceptibility $(\chi )$: Negative and very small.
• Examples: Copper, Bismuth, Silver, Gold, Water.

2. Paramagnetism

• Property: Weakly attracted by an external magnetic field.
• Cause: Magnetic dipoles tend to align along the applied field but only partially.
• Susceptibility $(\chi )$: Small positive value.
• Examples: Aluminium, Platinum, Sodium, Lithium.

3. Ferromagnetism

• Property: Strongly attracted by a magnetic field and can retain magnetism even after the field is removed.
• Cause: Large-scale alignment of magnetic dipoles in the same direction.
• Susceptibility $(\chi )$: Very high and positive.
• Examples: Iron, Cobalt, Nickel.

3.0Origin of Magnetism in Materials

• Atoms consist of electrons revolving around the nucleus.
• Each electron has orbital motion and spin motion, both of which contribute to a magnetic moment.
• In most atoms, these magnetic effects cancel each other.
• In certain materials, alignment of dipoles creates a net magnetic moment, leading to observable magnetism.

Thus, the origin of magnetism lies in the microscopic movement of charges.

4.0Basic Magnetic Quantities and Definitions

Magnetic Dipole

• A pair of equal and opposite magnetic poles separated by a small distance.
• Example: A bar magnet is a magnetic dipole.

Magnetic Dipole Moment (m)

• Defined as the strength of either pole multiplied by the distance between poles.
• Vector quantity directed from south pole to north pole of a magnet.

Magnetization (M)

• The magnetic moment per unit volume of a material.
• Describes how strongly a material is magnetized in an external field.

Magnetic Intensity (H)

• The applied magnetic field strength due to an external source (like a solenoid).
• Measured in A/m (ampere per meter).

Magnetic Induction (B)

• Also called magnetic flux density.
• Describes the actual magnetic field inside a material.
• Related to $(B={\mu }_0(H+M))$.

5.0Magnetic Properties of Materials

Diamagnetic Materials

• Very weakly repelled by a magnetic field.
• Do not retain magnetism after the field is removed.
• Magnetic susceptibility $((\chi ))$ is negative.
• Examples: Copper, Silver, Gold, Water.

Paramagnetic Materials

• Weakly attracted by a magnetic field.
• The effect disappears when the field is removed.
• Magnetic susceptibility is small and positive.
• Examples: Aluminium, Platinum, Sodium.

Ferromagnetic Materials

• Strongly attracted by a magnetic field.
• Can retain magnetism even after the field is removed (permanent magnets).
• Large and positive susceptibility.
• Examples: Iron, Cobalt, Nickel.

6.0Magnetic Susceptibility and Permeability

Magnetic Susceptibility $\left(x_m\right)$

${\chi }_m=\frac{I}{H}$ [It is a scalar with no units & dimensions]

Physically it represents the ease with which a magnetic material can be magnetised.

Note:- A material with more ${\chi }_m$, can be change into magnet easily.

Magnetic Permeability $(\mu )$

$\mu =\frac{B}{H}=\frac{\text{ Total magnetic field inside a material }}{\text{ Magnetizing field }}$

Unit of $\mu =\mu =\frac{B_m}{H}=\frac{Wb/m^2}{A/m}=\frac{\text{ Weber }}{A-m}=\frac{H-A}{A-m}=\frac{H}{m}$

It represents the degree up to which a material can be penetrated by the magnetic field lines.

Relative Permeability $\left({\mu }_r\right)$

${\mu }_r=\frac{\mu }{{\mu }_0}$

It has no units and dimensions

Relation between $\mu$ and ${\chi }_m$

When a magnetic material is placed in a magnetic field $\overrightarrow{B_0}$ for magnetization, then total magnetic field in the material is

$\overrightarrow{B_m}=\overrightarrow{B_0}+\overrightarrow{B_{in}}\left\{\overrightarrow{B_{in}}=\text{ induced field }\right\}$

$\because {\vec{B}}_0={\mu }_0\vec{H};\overrightarrow{B_{in}}={\mu }_0\vec{I}$

$\because \overrightarrow{B_m}={\mu }_0(\vec{H}+\vec{I})$

$B_m={\mu }_0(H+I)$

$\mu H={\mu }_{0}H\left(1+\frac{I}{H}\right)$

$\mu ={\mu }_0\left(1+{\chi }_m\right)$

$\frac{\mu }{{\mu }_0}=\left(1+{\chi }_m\right)$

${\mu }_r=\left(1+{\chi }_m\right)$

For vacuum, ${\mu }_r=1,{\chi }_m=0$

For air, ${\mu }_r=1.04,{\chi }_m=0.04$

7.0Hysteresis in Magnetic Materials

When a ferromagnetic material is repeatedly magnetized and demagnetized:

• The magnetization does not follow the same path during increase and decrease of field.
• The graph of ( B ) vs ( H ) shows a hysteresis loop.
• Key points:
• • Retentivity: Ability to retain magnetism.
  • Coercivity: Field required to demagnetize completely.
• Soft iron: low coercivity (used in transformers).
• Steel: high coercivity (used in permanent magnets).

8.0Earth’s Magnetism

Earth behaves like a huge bar magnet tilted slightly with respect to its rotation axis.

Magnetic Elements of Earth

1. Magnetic Declination (D): Angle between geographic meridian and magnetic meridian.

2. Magnetic Inclination (Dip): Angle between Earth’s magnetic field and the horizontal plane.

1. Horizontal Component (H): Component of Earth’s field along the horizontal plane.

Relation:

$B^2=H^2+Z^2$

where $(B)=$ total intensity, $(Z)=$ vertical component.

9.0Bar Magnet as an Equivalent Solenoid

• A bar magnet produces a magnetic field similar to that of a solenoid.
• Magnetic moment of a solenoid:
  $[\mathrm{M}=\mathrm{nI}\mathrm{A}]$ where ( n ) = turns per unit length, ( I ) = current, ( A ) = cross-sectional area.

This helps in theoretical treatment of bar magnets using solenoid concepts.

10.0Torque on a Magnetic Dipole in a Uniform Magnetic Field

Torque and Force on Magnetic Dipole

Torque on a Magnetic Dipole in Uniform Magnetic Field

When a bar magnet is placed in a uniform magnetic field the two poles experience a force. They are equal in magnitude and opposite in direction and do not have same line of action. They constitute a couple of forces which produces a torque. The torque tries to rotate the magnet so as to align it parallel too direction of field

Torque due to force couple

1. Bar Magnet

Consider a bar magnet of magnetic moment $\vec{M}$ held in a uniform magnetic field $\vec{B}$ making an angle $\theta$ with the field,then the magnet experiences a torque given by,

$\tau =\text{ force × perpendicular distance between force couple }$

$\tau =F(l\sin \theta )$

$\tau =(mB)(l\sin \theta )$

$\tau =ml(B\sin \theta )$

$\tau =MB\sin \theta ,\text{ where }M=ml$

$\vec{\tau }=\vec{M}\times \vec{B}$

$\tau =MB\sin \theta$

Case-1:If $\theta =90^{\circ }\Rightarrow \tau =MB(\text{ maximum })$

Case-2:If $\theta =0^{\circ }\text{ or }180^{\circ }\Rightarrow \tau =0\text{ (minimum) }$

2. Coil or Loop: If a loop carries a current of magnitude I and magnetic moment $\vec{M}$ held in a uniform magnetic field $\vec{B}$ making an angle \theta Then the loop experiences a torque given by

$\vec{\tau }=\vec{M}\times \vec{B}$

$\tau =MB\sin \theta$

$\vec{\tau }=I(\vec{A}\times \vec{B})$

If loop have N turns then

$\vec{\tau }=NI(\vec{A}\times \vec{B})$

$\tau =NIAB\sin \theta$

Case-1:If $\theta =90^{\circ }\Rightarrow \tau =NIAB(\text{ maximum })$

Case-2:If $\theta =0^{\circ }\text{ or }180^{\circ }\Rightarrow \tau =0\text{ (minimum) }$

Illustration-1. A magnetic Moment $50\hat{i}A-m^2$ placed along x-axis. When magnetic field is $\vec{B}=(0.5\hat{i}+0.3\hat{j})\text{ Tesla }$.The torque acting on magnet is:-

Solution:

$\vec{\tau }=\vec{M}\times \vec{B}$

$\left|\begin{array}{ccc}\hat{\mathrm{i}}& \hat{\mathrm{j}}& \hat{\mathrm{k}}\\ 50& 0& 0\\ 0.5& 3& 0\end{array}\right|=$

$(0)\hat{i}-(0)\hat{j}+(150)\hat{k}N-m=150\hat{k}N-m$

Illustration-2: A uniform magnetic field of 5000 gauss is established along the positive z-direction. A rectangular loop of side 20 cm and 5 cm carries a current of 10 A is suspended in this magnetic field. What is the torque on the loop in the different cases shown in the following figures? What is the force in each case? Which case corresponds to stable equilibrium?

Solution:

1. Torque on loop, $\tau =BIA\sin \theta$

Here $\theta =90^{\circ },B=5000\text{ Gauss }=5000\times 10^{-4}=0.5\text{ Tesla }$

$I=10\text{ Ampere, }A=20\times 5{\mathrm{cm}}^2=100\times 10^{-4}=10^{-2}{\mathrm{m}}^2$

Now $\tau =0.5\times 10\times 10^{-2}=5\times 10^{-2}N-m.Itisdirectedalong-Yaxis$

2. Same as$\text{ (a) }$

3. $\tau =5\times 10^{-2}N-malongx-direction$

4. $\tau =5\times 10^{-2}N-matanangleof240^{\circ }with+xdirection.$

5. $\tau$ is zero[∵ Angle between plane of loop and direction of magnetic field is $90^{\circ }$]

Resultant force is zero in each case. Case (e) corresponds to stable equilibrium.

Illustration-3:A solenoid of 200 turns/m is carrying a current of 5A. Relative permeability of core material of solenoid is 3000. Determine the magnitudes of the magnetic intensity, magnetization and the magnetic field inside the core.

Solution:

Magnetic Intensity $H=ni=200{\mathrm{m}}^{-1}\times 5A=1000{\mathrm{Am}}^{-1}$

${\mu }_r=1+\chi \text{ i.e }\chi =3000-1=2999$

Hence the magnetization $I=\chi H=2.999\times 10^6{\mathrm{Am}}^{-1}$

The magnetic field $B={\mu }_0{\mu }_{r}H=3000{\mu }_{0}H=3000\times 4\pi \times 10^{-7}\times 1000=3.769T$

Illustration-4: A rod of magnetic material of cross section $0.25{\mathrm{cm}}^2$ is located in $4000A/m$ magnetising field. Magnetic flux passes through the rod is $25\times 10^{-6}Wb$. Find out for rod

 (i) permeability

 (ii) magnetic susceptibility 

(iii) magnetisation

Solution:

 (i) Magnetic Flux $\varphi =BA\Rightarrow B=\frac{\varphi }{A}=\frac{25\times 10^{-6}}{0.25\times 10^{-4}}=1\mathrm{Wb}/{\mathrm{m}}^2$

 (ii) ${\mu }_r=1+{\chi }_m{\chi }_m={\mu }_r-1\left(\because {\mu }_r=\frac{\mu }{{\mu }_0}\right)$

${\chi }_m=\frac{\mu }{{\mu }_0}-1=\left(\frac{2.5\times 10^{-4}}{4\pi \times 10^{-7}}-1\right)=199-1=198$

(iii) magnetisation $I={\chi }_{m}H=198\times 4000=7.92\times 10^5\mathrm{A}/\mathrm{m}$

11.0Applications of Magnetism and Matter in Real Life

• Electromagnets used in cranes for lifting heavy loads.
• Transformers and generators use soft iron cores.
• Permanent magnets made of steel are used in electric meters, compasses, loudspeakers.
• Earth’s magnetic field helps in navigation using a magnetic compass.
• Data storage in hard disks uses magnetic domains.