Magnetism - a physical phenomenon associated with magnetic field which can be generated by electric current, motion of electric charges (including atomic orbital motion of electrons), intrinsic properties of elementary particles (e.g. electron spin moment), or combination of all of these factors.¹⁾²⁾ The name “magnetism” is often used interchangeably with “electromagnetism”.³⁾

Horseshoe magnet attracts iron filings through magnetic force

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However, electromagnetism has a much wider meaning, and refers to mutual relationship between magnetic field and electric field, which can be mathematically described with Maxwell's equations, under all conditions: static or dynamic.⁴⁾

Depending on the context, the term magnetism is sometimes used to differentiate magnetostatic (non-changing) fields from electromagnetic (varying), whereas in a wider context magnetism includes all magnetic phenomena (magnetostatic or electromagnetic).⁵⁾

In its narrower meaning, the term magnetism is used in relation to all microscopic and macroscopic phenomena which are useful for engineering purposes, such as generation of magnetic field, magnetic properties of materials (from easy magnetisable electrical steel to permanent magnets) and their applicability to construction of efficient magnetic circuits for electric motors, generators, and transformers.⁶⁾

Also, magnetism can mean a specific behaviour of a given material in response to some applied magnetic field. It is then said that the material exhibits a certain type of magnetism: ferromagnetism, paramagnetism, diamagnetism, etc.

From engineering viewpoint, materials which exhibit strong magnetic response are often referred to as “magnetic”, and those with negligibly weak interactions are “non-magnetic”. However, all atoms exhibit diamagnetic behaviour and magnetic field also penetrates vacuum. Hence, all matter exhibits some magnetic response and from a more fundamental view all materials are "magnetic" (even superconductors).

Magnetic force is the basis of operation of electric motors, generators, relays, actuators, loudspeakers, and similar electromagnetic devices.

Magnetic force due to magnetic poles, from left to right: like poles repel (position of the hanging magnet is deflected accordingly), opposite poles attract, nail (soft ferromagnetic material) gets magnetised and attracts either pole of a magnet, the force on non-magnetic materials (such as plastic and copper without electric current) is typically negligible, electromagnetic coil with current can repel or attract the magnet (depending on the polarity of current), and the force on non-magnetic stainless steel (e.g. type 316) is negligibly small

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See also the main article: Electromagnetism

The word magnetism is often used as a short-hand for electromagnetism, and in any sense of the word there is an inseparable link between magnetic field and electric field, at least because of the electric charges involved in current, or intrinsic property of electrons, called electron spin magnetic moment.⁷⁾

From theoretical physics viewpoint, and especially when introducing the topic to students, a distinction is made so these topics are treated in a sequence of increasing complexity, especially with the view of the associated mathematical equations (Maxwell's equations):⁸⁾⁹⁾

• electrostatic - static electric charges, only electric field, no electric current and no magnetic field; intrinsic magnetic moment of electrons is ignored
• magnetostatic - constant electric current, constant magnetic field, with the effects of electric field negligible
• electromagnetic - varying electric and magnetic field creates electromagnetic phenomena such as electromagnetic waves

From engineering viewpoint, magnetism is useful because it can be utilised for generating large mechanical forces and transformation of electricity with high power over vast distances. The efficiency of conversion (magneto-mechanical or electromagnetic) is aided by the use of suitable magnetic materials and therefore the meaning encompasses all such phenomena, from existence and generation of magnetic field, through its effect on materials, to the design of magnetic circuits. All these effects are electromagnetic as such, but most low-frequency engineering applications are not concerned with electromagnetic radiation, and therefore the magnetic component itself is the most important for the utilisation in practical applications.

Magnetic properties of materials are fundamental for design of energy efficient and cost-effective devices.¹⁰⁾¹¹⁾

Magnetostatics is a sub-domain of electromagnetism which deals with magnetic field which does not change (it has a constant value over time). Under such condition the electric field is also constant, and therefore no electromagnetic radiation is generated.¹²⁾ The electric field is considered only from the viewpoint of being an energy source for driving electric current.

However, strictly magnetostatic conditions are sometimes difficult to investigate, because due to the Faraday law of induction (one of the Maxwell's equations) electric voltage is induced only when there is some change of magnetic flux coupling into a given winding.

Therefore, some slow changes can be introduced, and if their effect is negligible from the view point of dynamic phenomena (such as eddy currents) then the behaviour can be still treated as static even though there are some changes - such conditions or sometimes referred to as magneto-quasi-static¹³⁾, or simply quasi-static.¹⁴⁾

See also the main article: Magnetic force

Magnetic force on a moving electric charge acts perpendicularly to the direction of magnetic field (for positive charges the path is affected in one direction, for a negative charge in the opposite, according to the right-hand rule). Magnetic force does not act on a stationary charge, or a charge moving in the direction of the magnetic field. Such force constitutes the definition of magnetic field B.¹⁵⁾

Also, the electric charge is accelerated in the direction of electric field.

These two components add vectorially producing the total force (called Lorentz force), expressed by:¹⁶⁾

Example of Lorentz force acting on a positively charged particle q: a) force F_e in electric field E acts along E, b) force F_m in magnetic field B acts perpendicularly to B, c) total force F = F_e + F_m in both fields; green arrows show the velocity component (solid) and general direction of movement (dashed)

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In most electromagnetic devices the force due to electric field is often negligible. Force due to electric field can also be utilised in devices such as electrostatic motors, but because of very high voltages required, and smaller forces produced the electrostatic component is of less practical importance, with some niche applications such as MEMS relays, or particle accelerators.¹⁷⁾

Magnetic field is generated by electric current in the winding of an electromagnet and it is concentrated in the air gap by magnetic material of the magnetic core

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There are three main sources of magnetic field, all inseparably connected to electric charges:

• moving electric charges constitute electric current which generates magnetic field
• intrinsic magnetic moments of sub-atomic particles, such as magnetic spin moment of electrons
• magnetic component of electromagnetic radiation (whose generation is also caused by interaction of electric charges)

If the electromagnetic radiation does not take place (e.g. at low frequencies) only the two sources are important.

Transmission and utilisation of electricity relies on macroscopic electric currents flowing in metal conductors. Whenever there is a current flow there is always some magnetic field generated around it. The amount of magnetic field due to current can be calculated from Ampere's circuital law or Biot-Savart law.¹⁸⁾

Ampere's law in the integral form describes the link between the electric current and the magnetic field circulating around it, scaled by the magnetic path length:

Electric current I generates magnetic field which can be quantified with magnetic field strength H

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Under certain conditions, for simple magnetic circuits (with well-defined path and no flux leakage) the equation can be rearranged and simplified to:

which lends itself for direct application in designs of magnetic circuits in motors, electromagnets, as well as sensors.¹⁹⁾

All materials respond to magnetic field in some way. This is also true for those materials which are commonly referred to as “non-magnetic”, whose response can be of much lower magnitude as compared to the “magnetic” ones. The magnetic response is also typically affected by other parameters, such as: temperature, pressure and mechanical strain, chemical composition, crystallography, and many more.²⁰⁾

In every day life the materials are often referred to as “magnetic” and “non-magnetic”. A simple test is to touch a given material with a permanent magnet (e.g. a fridge magnet) - if a mechanical force can be felt (e.g. the magnet “sticks”) then the material is “magnetic”, otherwise it is “non-magnetic”. This layperson classification does not follow the same classes as the theoretical - for instance a magnet does not attract antiferromagnetic material, but it is a magnetically ordered structure.

The magnetisation process takes place at the atomic, or even sub-atomic level, and depending on the microscopic behaviour can be classified in to one of several types of “magnetisms”.

See also the main article: Types of magnetisms.

A specific class of a response can be categorised as a type of magnetism, with the three principal ones: ²¹⁾

• paramagnetism
• diamagnetism
• ferrromagnetism (and other ordered structures)

And from theoretical physics point of view these can be further subdivided to over twenty other types, depending on the involved atomic structure, spin ordering, etc.

Geomagnetism is a study of Earth's magnetic field

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Also, there are multiple other terms which are commonly used in relation to other branches of science. These do not refer to phenomena different from those listed above, but strongly linked with the specific scientific or technological area, and with the topic being significant enough so it gained its own name:

• electromagnetism - branch of physics concerned with analysing magnetic and electric field as a single electromagnetic phenomenon ²²⁾
• biomagnetism - magnetic phenomena in living organisms ²³⁾
• geomagnetism - study of Earth's magnetic field ²⁴⁾
• paleomagnetism - magnetic properties of geological structures ²⁵⁾
• cryomagnetism - magnetic phenomena at very low temperatures ²⁶⁾
• micromagnetism - magnetic phenomena in small physical structures (e.g. at atomic level) ²⁷⁾
• quantum magnetism - magnetic phenomena in quantum physics²⁸⁾
• and many more.

Magnetic spin moments of electrons generate their own magnetic field which in ferromagnets (and other “ordered” magnetic structures, e.g. ferrimagnets) creates spontaneous alignment of such moments due to strong neighbour-neighbour interaction, leading to creation of magnetic domains, each of which is internally magnetised to saturation magnetisation even over macroscopic distances (even up to tens of millimetres).

However, over the whole volume of material the domains can be oriented in opposing directions, so that the magnetic energy is minimised and the material produces very little external magnetic field.²⁹⁾³⁰⁾

When some external field is applied the domains respond, change size and re-align, due to rotation of the individual moments, such that there is some net macroscopic magnetisation M, which adds up to the total response of the magnetic flux density B. The stronger the response the larger the B due to the applied H, and the proportionality between these two quantities is the magnetic permeability, which is a figure of merit for magnetic materials.³¹⁾

With sufficiently high magnetic field applied to a ferromagnet (or ferrimagnet) all the moments align to the field and the material saturates magnetically, because magnetisation cannot increase any further.³²⁾

H, B, M, and J in a ferromagnet

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Magnetic domains in a single grain (outlined with a black line) of non-oriented electrical steel. The photo shows an area 0.1 mm wide, and the arrows show orientation of the domains. The domains are separated by domain walls

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Magnetic domain structure (lancet combs switching during magnetisation) in high-permeability grain-oriented electrical steel. Bar domains are visible in the upper part. ^{Copyright © Oles Hostanar}

Hysteresis loop is a symbol of non-linear ferromagnetic phenomena, for high values showing the effect of magnetic saturation

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Soft, hard and semi-hard magnetic materials (as well as non-magnetic) are used in magnetic hard drives

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Ferromagnets and ferrimagnets are used extensively for several purposes:

• soft magnetic materials (easy to magnetise, low coercivity) - for construction of magnetic circuits in order to concentrate and guide the magnetic flux
• hard magnetic materials (difficult to magnetise and demagnetise, very high coercivity) - for storing magnetic energy and thus making permanent magnets which behave as “passive” sources of magnetic field
• semi-hard magnetic materials (medium coercivity) - for information storage (magnetic hard drives) and manipulation of forces (e.g. electropermanent magnet)

All non-magnetic materials have very weak neighbour-neighbour interaction for the electrons, so the magnetic domains do not form, and only the individual contribution of each atom takes place, which due to thermal agitation is highly randomised and thus largely cancelling over macroscopic distance. Only with very precise measurements it is possible to distinguish between paramagnets (weak positive response) and diamagnets (weak negative response). Every single atom exhibits the diamagnetic response, but it is overshadowed by the stronger paramagnetic or much stronger ferromagnetic behaviour.³³⁾

However, all magnetic materials (ferromagnets and ferrimagnets, soft, semi-hard and hard) become paramagnetic (reversibly) at sufficiently high temperatures.³⁴⁾

The magnetic force can be directed to generate useful torque. If a frame of wire with current is placed in magnetic field (as illustrated) then the force acts on the two sides of the frame in opposite directions, thus developing a torque. The force acts according to the right-hand rule and for the diagram as illustrated the frame will rotate in the clockwise direction.

Force in a simple commutated motor follows the right-hand rule: if the index finger shows the direction of current $I$ (which moves the charge $q$) and the middle finger shows the direction of magnetic field $B$, then the thumb shows the direction of magnetic force $F$ acting on the moving charge; the force is proportional to the length of wire $l$ exposed to the magnetic field

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For the side of the frame near the S pole, the force will point upwards, scaled by the length of the active wire, adding up to the total value of:

For the other side of the frame the force has same value but it points downwards, so the frame rotates delivering useful torque which can be delivered to some external machine via shaft attached to the frame.

The force arises because of the interplay of the magnetic field between the magnetic poles N-S and the magnetic field produced by the current flowing in the frame.³⁵⁾

However, at the topmost position the direction of current in the frame has to be changed for the motion to continue. This can be achieved with the commutator (half-rings in the image) which is physically mounted to the rotating frame. The current is connected via brushes which slide on the surface of the commutator.

Typical induction motor supplied by 3-phase AC current

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The commutated motor is just one of the many possible solutions of developing useful torque. The magnetic field can be generated by permanent magnets or electromagnet-like windings, creating magnetic poles. These can be positioned both on the stationary (stator) or rotating part (rotor), with the rotor inside, outside or sideways (axially) with respect to the stator.

The interaction can be improved by using magnetic material inside the rotating frame so that magnetic field generated by the frame with current is “concentrated”, making use of the high magnetic permeability of magnetic materials.

Depending on the specific design, commutated motors can be used with DC or AC current. However, brushes create energy losses due to friction and arcing, and for low-power applications brushless motors were also developed. Reluctance motors employ suitably switched electromagnets (magnetic poles) and some magnetic material, which gets magnetised and attracted into the field, after which another coil is switched on and the process continues. Majority of inexpensive motors in industrial applications are induction motors.³⁶⁾

Electromagnetic actuators operate on the same basic principles as motors, it is just that the design is typically focused on producing force acting along a straight line or some other path, rather than circular rotation. Motors can be treated as a special case of actuators.

The mechanical force is then used for working with or against other forces, as for example mechanical springs which are used to provide the returning force when the winding or electromagnet is switched off.

A few examples of magnetic forces acting in devices can be given as:

• fridge magnet - working with friction against gravity
• loudspeaker - balancing spring force acting on the membrane
• relay - acting against internal spring to connect or disconnect electrical contact
• compass - aligning the needle against friction
• ferrofluid - mechanical forces act on the particles suspended in a fluid and change its behaviour (e.g. against gravity)
• magnetic levitation and magnetic bearing - suspending mass in a contactless way

Permanent magnets are used in motors, generators, actuators, loudspeakers, toys, etc.

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Typical relay

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Deflection coils in a CRT affect trajectory of charged particles

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Faraday's law of induction - changing magnetic field (flux density B or flux Φ) by moving the magnet induces electromotive force EMF (measurable as voltage V) in a loop of conductor; the voltmeter needle deflects in opposite directions if the magnetic field is increasing or decreasing

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The Faraday's law of induction states that the amount of electromotive force (EMF) induced in a closed loop or winding is proportional to the number of turns and the rate of change of magnetic flux penetrating such loop. Flux density is linked to the flux through the area, so the equation can be written in either of the formats as shown below, as well as in a differential or integral forms as used in vector calculus notation.³⁷⁾³⁸⁾

The application of this law if fundamental for operation of all electric generators, transformers, as well as many transducers and sensors.³⁹⁾

Simple generator with a commutated rotor, illustrated wit the right-hand rule: if the index finger shows the direction of velocity $v$ of the charge $q$ displacement (due to conductor movement) and the middle finger shows the direction of magnetic field $B$, then the thumb shows the direction of the magnetic force $F$ acting on the charge and inducting the electromotive force EMF

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If the wire frame of the rotor does not have any current supplied to it, but is made to rotate (e.g. by an external energy source such as handle or wind turbine), then electromotive force (EMF) will be induced which will appear as voltage at the commutator connections, and hence it will be available to the external circuit. The voltage amplitude will be proportional to the magnitude of the magnetic field, length of active wire and speed of rotation, according to the Faraday's law of induction (described below).

This principle is used in all high-power electromagnetic generators, which convert mechanical into electrical energy. Most motors can operate as generators, so there can be also many types of generators, for smaller power also called dynamos and alternators.⁴⁰⁾

Commutated rotors can be used to generate DC-like pulsating current, but other designs are possible too. High-power generators (in power plants) operate as synchronous generators producing AC voltage, with their rotors excited by a regulated DC current, so that the amplitude of the generated voltage can be precisely controlled.

The laws of electromagnetism are used for design of electromagnetic coupling of energy between the source and the load. Although some mechanical effects can be generated during the operation (e.g. magnetostriction) the energy is converted primarily through non-moving parts, owing to electromagnetic induction. This is therefore a different application from motors and generators. Examples:

• transformer - converting one level of variable current to a different level
• wireless charger - delivering energy in a contactless way

There are also other processes, which can transfer electromagnetic energy into a different type of energy (e.g. heat) but the electromagnetic-electromagnetic conversion is a special case, and it is currently used as the pivotal component of national and international grids supplying electricity. This is possible because the transformers can increase the voltage to very high level for more efficient transmission of electricity. At the same time the transformers are very efficient devices, with figures up 99% for high-power devices.⁴¹⁾

Another inherent feature of electromagnetic conversion is that it allows galvanic separation between the circuits, which is a very important factor from the viewpoint of safety of electric circuits.⁴²⁾ For example, mains-powered chargers for portable appliances (such as mobile phones, tablets, laptops) are not required to have connection to earth only if they have full galvanic isolation between the mains input and the low-voltage output.⁴³⁾ Some portable power tools which need to be supplied from mains make use of galvanic separation through transformers operating at extra-low voltage.⁴⁴⁾

See also: Transformer.

Transformers are used extensively in distribution of electricity at the national and even continental level. For example, most European countries are interconnected into one grid operating at a synchronised frequency of 50 Hz (60 Hz in USA and some countries).

Power transformer is a crucial part of electric grid ^{by Marvin L. Daniels, U.S. Army, Public domain}

Transformers are extremely useful devices, because they have no moving parts directly involved in the energy conversion process, and can change one level of voltage or current to another level.

Operation of power transformers is based on several interlinked principles, most of them involving electromagnetics to a greater or lesser extent.⁴⁵⁾ The following sequence can be thought of, for the transformer to deliver power to the load connected to its output:

1. AC voltage is applied to the primary winding
2. primary voltage applied across the impedance of the primary winding creates primary current (Ohm's law)
3. primary current sets up magnetic field strength H in the magnetic core (Ampere's circuital law)
4. materials in the magnetic core respond to H with magnetic flux density B (magnetic properties of materials, laminated cores to reduce eddy currents)
5. B in the core penetrates the secondary winding (advantage of magnetic core guiding the magnetic flux)
6. EMF is induced in the secondary winding due to changing B (Faraday's law)
7. EMF appears as voltage at the output terminals of the secondary winding (Kirchhoff's voltage law)
8. voltage applied to the load at the output makes current (Ohm's law)

Switch-mode power supply, with several inductive components: common-mode choke, PFC inductor, resonant transformer, and filter inductor

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Many topologies of switch-mode power supplies rely on magnetic components such as high-frequency transformers (operating similarly to ordinary transformers), but also inductors or coupled-inductors. The latter ones utilise the energy stored in the magnetic field, for one cycle of switching, to facilitate the conversion of voltage or current level.

Switch-mode power supplies of various sizes and configurations are ubiquitous in all consumer electronics: computers, monitors, mobile phones, TVs, etc.

Switch-mode converters are also used for much higher power (tens or even hundreds of kW) converting DC voltage (e.g. from photovoltaic panels) into AC voltage which can be fed to the mains grid.

Planar coils for wireless charging (top and bottom sides) for low power application such as mobile phone

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Wireless chargers operate on the same principle as transformers, but with much weaker magnetic coupling between the primary and secondary winding, due to the relatively large air gap between them.

Large amount of reactive power is present in the windings which does not take a direct part in the energy conversion process. Therefore, for improved efficiency both windings are typically made to resonate with a local capacitor, so that the voltage source does not have to drive the full reactive power at all times.

There are several applications in which magnetism is used for creating thermal effects. Only few of these exhibit a direct link between magnetic field and thermal phenomena, rather than having some additional intermediate processes involved.

Electromagnetic heating relies on some intermediate physical phenomena to generate heat. For instance, electric current is induced in any conducting medium which is exposed to a varying magnetic field.

Induction heating of a metal bar, which is hot enough to glow (melting is also possible) ^{by Vector1 nz, CC-BY-SA-3.0}

These so-called eddy currents are capable of heating up the medium in which they flow, and it is a basis for all induction heating devices. However, it is the eddy currents which are the direct source of heat - so electromagnetism is used only to transfer the energy and induce the currents.

Examples:

• induction heating - heating by inducing eddy currents
• microwave heating - heating by friction due to mechanical movements of water particles

Electromagnetic cooling is much more difficult, but it can be achieved by adiabatic demagnetisation and the magnetocaloric effect. In theory it should be possible to build efficient magnetic refrigerators, without any moving parts. Research is carried out to find appropriate materials and configurations which could facilitate commercially viable devices.⁴⁶⁾

Examples:

• magnetocaloric effect - cooling through demagnetisation
• Nernst effect - generation of temperature gradient due to magnetic field

Compass detects the direction of Earth's magnetic field

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A multiplicity of other physical quantities can be measured by employing phenomena related to magnetics. In sensors and transducers the amount of processed energy is usually small, and focus is given to such aspects as accuracy and linearity of signal transformation, rather than efficiency of energy conversion.

Fluxgate magnetometer is a sensor of magnetic field

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Examples:⁴⁷⁾

• Hall effect - output voltage is proportional to the input magnetic field (or electric current which produces it)
• Faraday effect - light twisting angle is proportional to the input magnetic field (or electric current)
• fluxgate magnetometer - asymmetry of magnetic saturation of one element can be used as a basis for measurement of magnetic field from a different source (e.g. electric current)
• Kerr effect - magnetic domain wall movements can be used as a detector of magnetic field (or electric current)
• compass - sensing direction of Earth's magnetic field
• magnetic resonance imaging - electromagnetic field generated by protons can be used for construction of 3D images of inside of living organisms in a non-invasive way (however this application involves high-frequency magnetic field and it belongs more to the domain of electromagnetism).

• Electromagnetism
• Magnetic field
• Magnetic field strength H
• Magnetic flux density B
• Confusion between B and H