# Introduction to Magnetism: Ferromagnetism & Magnetic Fields

This topic is part of the HSC Physics course under the section Magnetism.

### HSC Physics Syllabus

• investigate and describe qualitatively the force produced between magnetised and magnetic materials in the context of ferromagnetic materials (ACSPH079)
• investigate and explain the process by which ferromagnetic materials become magnetised (ACSPH083)
• apply models to represent qualitatively and describe quantitatively the features of magnetic fields

### What is Magnetism?

Many materials are magnetic, allowing them to interact with each other. As you may be aware, opposite (North and South) poles attract, and like poles repel.

'North' and 'South' are used to denote the polarity of magnets and magnetic fields (discussed below) because the North pole of a compass needle always points to the cardinal North pole of Earth. This is because Earth produces its own magnetic field, and the directional North pole is actually its magnetic South pole which attracts the North pole of a magnet such as the compass needle.

At the atomic level, magnetism primarily arises from two sources: the orbital motion of electrons around the nucleus and the spin of the electrons themselves. Each electron behaves like a tiny magnet, with its own magnetism.

### What is Spin?

"Spin" is a somewhat misleading term because it suggests a physical spinning motion around an axis, which is not accurate at the quantum level. Instead, spin is an intrinsic form of angular momentum carried by fundamental particles, including electrons, protons, and neutrons.

Spin is a fundamental quantum property of particles, much like charge or mass. It's an intrinsic feature, meaning it's a built-in property of the particle, not due to any external motion.

While we can't visualise spin as a literal spinning motion, we can use arrows or vectors in diagrams to represent the direction of a particle's spin and its magnetic moment. When two electrons occupy the same orbital in an atom, they must have opposite spins (a requirement known as the Pauli Exclusion Principle). This spin-pairing can lead to magnetic neutrality in some materials, as the opposing spins cancel out each other's magnetic effects.

#### Electron Spin

The magnetism of a material is primarily due to the electron spin and orbital motion of electrons around the nucleus. Electrons are the primary charge carriers in atoms, and their motion generates the most significant magnetic effects in materials.

#### Proton Spin

While protons do have a spin and an associated magnetic moment, their contribution to the magnetism of a material is usually negligible compared to that of electrons. This is due to their much larger mass and the fact that they are tightly bound within atomic nuclei, making their magnetic moments less influential on the material's overall magnetic properties. The proton's magnetic moment is relevant in nuclear magnetic resonance (NMR) but not typically in the magnetism of materials.

#### Neutron Spin

Neutrons also have spin and an associated magnetic moment, despite being neutral particles. The neutron's magnetic moment arises from the charged quarks that make up the neutron and their spins. However, like protons, the contribution of neutrons to the macroscopic magnetic properties of a material is generally insignificant compared to the effects of electrons.

In summary, while both protons and neutrons have spin and associated magnetic moments, the magnetism we observe in everyday materials is largely due to the behaviour of electrons.

### What is Ferromagnetism?

Ferromagnetic materials, such as iron, cobalt, nickel, gadolinium and some of their alloys, have an extraordinary ability to become magnetised. This means they can be transformed into magnets themselves.

Atoms in ferromagnetic materials, like iron, cobalt, and nickel, have unpaired electrons have spins that can align parallel to each other, creating a strong, cumulative magnetic field. When the magnetic fields of multiple of such atoms align in the same direction, this is referred to as a magnetic domain.

### Magnetic Domains

Vectors can be used to denote the collective direction of magnetic moments of atoms in a region of a ferromagnetic material.

A magnetic domain is a region within a ferromagnetic material where the magnetic moments of atoms (primarily due to electrons) are aligned in the same direction.

In an unmagnetised piece of ferromagnetic material, these domains are randomly oriented, so their magnetic effects cancel out, and the material has no large-scale magnetism.

### How Do Ferromagnetic Materials Become Magnetised?

When a ferromagnetic material is placed in an external magnetic field (produced by another magnet), the following occurs:

1. Domain Alignment: The magnetic moments of domains that are not aligned with the field tend to reorientate to become aligned.
2. Domain Growth: Domains aligned with the field grow at the expense of others as the boundary between domains moves.
3. Saturation: If the external field is strong enough, the material reaches saturation, where all domains are aligned, and the material is fully magnetised.

Although ferromagnetic materials can be magnetised to become permanent magnets, their ferromagnetism is not entirely permanent; if the external field is removed, some domains may become misaligned, resulting in a loss of magnetism over time. In contrast, magnetism of non-ferromagnetic materials (e.g. paramagnetism) quickly disappears after the external magnetism field is removed.

When magnetised, ferromagnetic materials are strongly attracted to magnets. These materials exhibit ferromagnetism below a certain temperature called the Curie temperature. Above this temperature, they lose their ferromagnetic properties.

### Magnetic Field Lines

Magnetic field lines of a permanent magnet are drawn from the south pole to the north pole inside the magnet, and from the north pole to the south pole outside the magnet. The density of field lines indicates field strength B.

Magnetic fields are visualised using magnetic field lines, which are imaginary lines that represent the direction and strength of the magnetic field.

Magnetic field strength

• is represented by the symbol B
• has the SI unit Tesla (T)

Magnetic field lines provide information on:

• Direction of magnetic field: Magnetic field lines emerge from the north pole of a magnet and enter the south pole.
• Strength of magnetic field: Like electric fields, the density of magnetic field lines indicates the strength of the field. The closer the lines are to each other, the stronger the magnetic field in that region.

Since magnetic fields exist in three dimensional space, we use 'crosses' and 'dots' to denote their directions when they project into and out of the page/screen respectively.

The magnetic field lines between two magnets illustrate the forces at play and depend on the orientation of the magnets relative to each other.

When the north pole of one magnet faces the south pole of another:

1. Direction: The magnetic field lines exit the north pole of one magnet and enter the south pole of the other magnet. This creates a loop from one magnet to the other.

2. Strength and Density: The field lines are densest between the two poles, indicating a strong magnetic force. This is where the attraction is strongest.

3. Shape: The lines form an arched pattern, bulging outwards before curving back into the opposing pole, illustrating the directional flow of the magnetic field.

When like poles of two magnets are near each other:

1. Direction: Magnetic field lines emerge from both north poles (or south poles) and curve away from each other, as like poles repel.

2. Strength and Density: The field lines do not connect between the two magnets but rather spread outwards and around each magnet. The density of the lines near the poles indicates the strength of the repulsive force.

3. Shape: The lines exhibit a spreading pattern, as they diverge from each pole. This pattern demonstrates how like poles push the field away, causing a repulsive force.

### Magnetic Fields vs Electric Fields

Electric and magnetic field lines are conceptual tools used to represent and visualise the invisible forces exerted by electric and magnetic fields. They have several similarities and differences:

#### Similarities:

• Directional Flow: Field lines for both electric and magnetic fields have directionality. Electric field lines point from positive to negative charges, while magnetic field lines exit from the north pole of a magnet and enter the south pole.

• Density: The density of field lines indicates the strength of the field; a greater concentration of lines corresponds to a stronger field.

• Continuous Lines: In ideal representations, both types of field lines are drawn as continuous lines without any breaks, representing the continuous nature of these fields.

• Influence by Medium: Electric field lines can be influenced by the dielectric properties of the medium they pass through, which can cause them to bend or change in density. Magnetic field lines are affected by the permeability of the materials they encounter, causing them to bend towards materials with higher permeability (such as ferromagnetic materials).

#### Differences:

• Sources: Electric field lines originate from positive charges and terminate on negative charges. In contrast, magnetic field lines always form closed loops, exiting from the north pole of a magnet and entering the south pole, continuing through the magnet back to the north pole.

• Monopoles: Electric charges can be isolated, resulting in field lines that start or end on single charges (monopoles). Magnetic field lines do not start or end on magnetic monopoles, they always exist in dipoles.

• Field Creation: Electric fields are created by electric charges at rest or in motion, while magnetic fields are created only by moving charges (electric currents) or changing electric fields (Maxwell's theory of electromagnetism).