Electron (e) - a fundamental sub-atomic particle which has the intrinsic property of a negative elementary electric charge.¹⁾

An electron is a part of every atom, with the number of electrons corresponding to the number of protons (atomic number), so that their electrical charges balance out and an atom can be electrically neutral.²⁾

Electron
Electric charge:3) -1.602 176 634 × 10-19 C
Mass:4) 9.109 383 7015 × 10-31 kg
Magnetic moment:5) -9.284 764 7043 × 10-24 J/T -1.001 159 652 181 28 μB
Spin: ½
Antiparticle: positron

Electron's mass is only around 1/1836 of proton's, despite both having equal but opposite electric charge.⁶⁾ For this reason, electrons contribute to less than 0.1% of the mass of atoms.

Electric and magnetic properties of electrons, as well as their electromagnetic interactions dictate many properties of matter, obviously electrical, electronic and magnetic, but also chemical properties.

The small size of electrons allows obtaining much finer resolution of an electron microscope than it is possible for an optical microscope.

The name “electron” was proposed by G.J. Stone in 1894, and the electron was discovered by J.J. Thompson in 1897. Electron's mass and charge were measured by R.A. Millikan and H. Fletcher in 1909.⁸⁾

Microscopic properties of an electron have been extensively studied since its discovery. However, because of its very small size there are no experimental techniques which allow direct “probing” or visualising in the same sense as it is possible to observe some small structures under an optical microscope.⁹⁾

Many properties of electrons, such as electric charge or spin are detectable or measurable. It is possible to describe the rules by which they are bound, but it is not possible to explain the reason for their existence, and therefore they are assumed to be “fundamental” particles, with fundamental properties.

Size of a particle has meaning in classical physics. However, at very small scales the quantum effects begin to play a significant role and it difficult to define the meaning of “size” of the assumed spherical object. It is not straightforward to agree even on methodology which should be used for definition, calculation or measurement.¹⁷⁾¹⁸⁾ Measurements at decreasing scales require larger energies, which can produce additional particles and thus confuse the outcome of the measurement.

Wilczek (2013):¹⁹⁾
Attempts to pin down an electron's position more accurately than this require, according to the uncertainty principle, injecting the electron with so much energy that extra electrons and anti-electrons are produced, confusing the identity of the original electron.

Depending on the approach there can be several radius definitions for the electron:²⁰⁾

• classical electron radius
• Compton radius
• quantum-mechanical Compton radius
• QED-corrected quantum-mechanical Compton radius
• electric charge radius
• observed QED charge distribution for a bound electron
• magnetic field radius

By using known physical constants and experimental data, the calculations based on these different approaches can give estimates which differ by several orders of magnitude.^21)22)23)

Consequently, the question “What is the size of the electron?” remains one of the unanswered questions in physics.²⁴⁾

Also, the internal structure of electrons is unknown. It is generally accepted that it is a point-like particle. However, there are many alternative theories, for example such that propose an electron to be composed of two massless particles orbiting each other at the speed of light.²⁵⁾ Some recent experiments appear to indicate more complex structure of electrons.²⁶⁾ The understanding of the internal structure of protons is also evolving with new experimental data.²⁷⁾

See also the main article: Electric charge.

Schematic representation of electrostatic field of a stationary negative charge, by using electric field lines

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Scientists can describe, but still cannot explain what exactly is electric charge. However, it is sufficient for such a basic property that it exists, it has some physical meaning and is measurable within the given system of units.²⁸⁾

An electron possesses an elementary amount of negative electric charge e. Its value is a physical constant, expressed in the SI system precisely (zero uncertainty) as:²⁹⁾ -1 e = -1.602 176 634 × 10^-19 C, and electric charge of other bodies can be expressed as integer multiples of it.³⁰⁾

Only such sub-atomic particles like quarks are thought to have electric electric charge in non-integer quantities e.g. -1/3 e or +2/3 e, but they only exists in configurations which add up to integer values of charge. For example, proton comprises three quarks (up, up, down), which add up to +1 e. Therefore, in any macroscopic application the charge is always quantised by the elementary amount of 1 e.³¹⁾³²⁾

An electron in isolation is an electric monopole - it is a source of electric field. By convention, it is assumed that that imaginary electric field lines begin at positive charges and terminate at negative charges.³³⁾

Like charges repel, opposite charges attract, causing mechanical forces which act on the charged bodies. This can be referred to as the electrostatic force, because it exists always, even if the charges remain stationary. This is different from magnetic or electromagnetic forces, which arise when the electric charges are in motion.

A neutral body can become polarised in electric field, by means of electrostatic induction, without the need for the charges to exchange between the bodies.

Opposite charges attract, like charges repel, neutral bodies generate no force (grey) but neutral bodies in the presence of other charges can become locally polarised due to electrostatic induction such that some force will occur

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In an atom, the nucleus comprises protons and neutrons, held together by the strong force. Electrons are bound to the nucleus by the electrostatic force. The electrons are organised in shells, subshells, and orbitals.

Diagram of electron structure in an atom: shells, subshells and orbitals, with an example of orbital occupancy for iron

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Subshells are grouped in shells, with number 1 being the innermost (or letter K, depending on the nomenclature, both naming conventions are in use). The numbering is linked to the energy levels.

In some literature the names “shell” and “subshell” are used interchangeably, or the distinction between shells and subshells is not explicitly made (but there is an implicit assumption that they exist).³⁴⁾³⁵⁾

Electron is excited to a higher energy state (higher subshell or shell) by absorbing a photon, and photon is released when electron drops to a lower energy level

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Electrons can transition to a higher energy level (higher subshell or shell) by absorbing a photon (a quantum of electromagnetic radiation). Conversely, if there is an empty position on a lower energy level, an electron can jump down, by emitting a photon.³⁶⁾

The lowest energy state (ground state) is when all the electrons are at the lowest possible orbitals. An atom will de-excite itself to the ground state if no energy is supplied to it, by emitting photons.

Heat represents energy, which excites atoms above the ground state. So any atom in a temperature higher than absolute zero (0 K) continuously gets excited and emits photos, producing photons of different wavelengths, corresponding to the excitation energy and energy of transition between the internal energy levels. Low energy corresponds to long wavelength (infrared), high energy to short (visible light, ultraviolet). Therefore, all matter emits radiation as a function of temperature, which is the basis for pyrometry.

Quantum restrictions dictate that there can be no two particles with the same set of quantum numbers in the same region of space (Pauli exclusion principle).

Orbitals overlap and penetrate each other, forming a spherical shape

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Therefore, each orbital can contain at most two electrons, because they can have different spin values (-1/2 and +1/2).

The orbitals are organised in subshells denoted with letters: s, p, d, f, etc., such that a given subshell contains a full set of orbitals, as dictated by the given set of quantum numbers. Higher-order subshells can hold more electrons, such that: s = 2, p = 6, d = 10, f = 14, and so on.

The orbitals within a given subshell overlap and penetrate each other so that their probabilities add up to a spherical shape.

The binding energy is the strongest for the innermost subshells and shells, and it is said that these shells are filled with electrons first.

The higher subshells (and shells) are not filled in a linear order, because there are numerous interactions which take place: electrostatic repulsion, interaction of spins, spin-orbit coupling, and so on. The interactions are very complex, and it is not possible to solve the Schrödinger equation analytically for a general case. Numerical methods are employed instead.³⁷⁾

For example, the 4s subshell is filled before the 3d shell, as dictated by the energy conditions (see also Hund's rules). One of the rules is such that in a given subshell each orbital is filled first with a single electron, and only when all orbitals have at least one electron the second electron is added. The opposing spins in such pairs precisely compensate out each other and they do not contribute to the magnetic moment of the whole atom. Only the unpaired electrons are significant magnetically.³⁸⁾

Quantum mechanics is complex and the various quantum phenomena are usually introduced with illustration of analogies involving some classical physics, for the ease of understanding. The sequence of analogies often follows the way the understanding of the inside of the atom was developed over the years.

In a simple Bohr atom model, the negatively charged electrons are point-like particles which orbit positively charged nucleus, in a similar way as planets orbit around the Sun. However, circular orbits would require continuous acceleration of a particle requiring radiation of electromagnetic energy, and such orbiting electron would very quickly lose all the energy and collapse onto the nucleus. This is one of the reasons why the name orbital was introduced (to distinguish it from orbit).

Therefore, all such simplified illustrations should be used used only as an aid for explanation and do not represent what actually happens inside an atom.

The exact mechanics of how electrons move around the nucleus remains unknown. From experiments and calculations it is now understood that electron presence is spread over a volume of space called orbital. There is no well-defined movement involved, it is only said that at a given point in space there is certain probability of finding an electron.³⁹⁾

Atom of helium: blue - spherical orbitals of electrons (size around 100 pm), red - protons, grey - neutrons (size of nucleus is around 1 fm) ⁴⁰⁾⁴¹⁾

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The probability distribution, for electrons in an atom, can be calculated from the Schrödinger equation $HΨ = EΨ$⁴²⁾, which for example for spherical coordinates can take quite a complicated form:⁴³⁾

$$ \left[ -\frac{{\hbar}^2}{2m_e} \left( \frac{∂^2}{∂ r^2} + \frac{2}{r}\frac{∂}{∂r} - \frac{1}{{\hbar}^2 r^2} \boldsymbol{{\hat{l}}^2} \right) - \frac{Z e^2}{4π ε_0 r} \right] \psi_i = ε_i \psi_i $$

(where the symbols are defined as in eq. (4.4) in Coey (2010)⁴⁴⁾; this equation is shown here only as an example). Computer software can be used for calculation and visualisation of the results.⁴⁵⁾

The low-order orbitals are spherical, but higher quantum numbers produce increasingly complex three-dimensional shapes. If the data is plotted as calculated, then such probability distributions produce fuzzy images, which are difficult to visualise and interpret. The probability does not stop at a specific distance, but the function extends to infinity, reducing the probability in some non-linear way.⁴⁶⁾

For this reason, a number of simplifications is used in order to increase clarity of images. For example, planes, cones or spheres can be used to indicate locations of “nodes” (places where function reduces to zero). Cross-section view can be employed as well.

However, the simplest method appears to be to use “hard shape” with a specific limit. For example, the volume were probability is greater than 90% is plotted with full opacity, and all other is shown as completely transparent. Also, there could be some additional scaling factors which can make easier to indicate intricate details of a given shape.⁴⁷⁾⁴⁸⁾

The red and blue colours in the images denote the positive and negative phase of the function. Any other colours can be used the represent the same information.

An example of a 4d orbital. The probability distribution is smeared over space so a 2D image is fuzzy and difficult to interpret. Cones represent “nodes” with zero probability, “solid” shapes are used for better visualisation of the shapes of orbitals, but their appearance depends on scaling factors even though all represent the same input data.⁴⁹⁾⁵⁰⁾

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Complexity of orbitals increases for higher order orbitals (just some typical examples are shown here for illustration)⁵¹⁾⁵²⁾

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Demonstration of standing waves on vibrating circular plate, with radial nodes (circles) at lower frequencies, and angular modes (with “spokes”) at higher frequencies ^{by P. Flowers, W.R. Robinson, R. Langley, K. Theopold, OpenStax.org, CC-BY-4.0}

The complex shape of orbitals can be explained with an analogy to vibrations of a body, with higher harmonics forming more complex shapes. An example is shown with a plate which can be made vibrating at different frequencies.

At lower frequency of vibration only concentric rings are present, representing standing waves, with clearly visible “nodes” (no displacement). But the higher the frequency the more complex shapes are created, including “spokes” forming at equally spaced angles.⁵³⁾

Similar vibration patterns can be expected for a spherical body, but with the standing waves extending over thee-dimensional space.

Magnetic moment of an electric current flowing in a loop can be expressed as the product of the amplitude of the current and the area of the loop.

In an atom, an electron orbiting around the nucleus represents a moving electric charge which is equivalent to electric current, but it must be remembered that by convention, the direction of electric current (blue arrow of $I$ in the image) is opposite to the direction in which the electron moves (green arrow of $v$). For this reason the vector of magnetic dipole moment of an electron points in the opposite direction to the angular moment.⁵⁴⁾

The orbit would represent a circle with some area. Therefore, in from the classical physics viewpoint there would be a magnetic moment associated with the orbital motion of an electron, in a loop without resistance,⁵⁵⁾ (inside the atom, electron moves effectively in vacuum so it can move freely).

The analogy of orbital moment is an electron orbiting the nucleus on a circular orbit (left) and for spin the sphere spins around its own axis (right)

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The orbital magnetic moment for the so-called first Bohr orbit can be calculated as: $μ_{orb} = \frac{e·h}{4·π·m}$ = 9.274 × 10^-24 A·m² ≡ J/T (where: e - electron charge, h - Planck constant, m - electron mass), which is exactly equal to Bohr magneton μ_B.⁵⁶⁾

Such orbital movement would have a “mechanical” angular momentum associated with it. A linear or angular momentum is a conserved quantity and energy must be exchanged in the system for it to change. Momentum is a product of mass and speed (rotational speed), and it is related to inertia of the body.⁵⁷⁾

The angular momentum due to orbital movement of an electron is $\boldsymbol{l} = m · \boldsymbol{r} × \boldsymbol{v}$, where: m - electron mass, r - orbit radius, v - velocity.

There is a fixed proportionality between the electron's charge e, orbital magnetic moment $μ_{orb}$ and angular momentum $\boldsymbol{l}$, such that: $μ_{orb} = - \frac{e}{2·m} · \boldsymbol{l}$. Because only physical constants are involved in the above equation, it can be written that $μ_{orb} = γ·\boldsymbol{l}$, where γ is the gyromagnetic ratio, equal to 1.761 x 10¹¹ Hz/T.⁵⁸⁾ (Gyromagnetic ratio is a quantity different from g-factor, which is unitless. For orbital motion the g-factor is exactly 1, but for spin it greater.⁵⁹⁾⁶⁰⁾)

The orbital angular momentum is quantised, in units of $\boldsymbol{l}$ (for orientation) or units of $\hbar$ (for value of component along the acting magnetic field).⁶¹⁾

However, electrons do not follow circular orbits, and orbitals which can take quite complex 3D shapes especially for higher orders, as described above.

In chemical compounds there is electrostatic interaction between the ions in molecules, and the contribution of orbital momentum is much smaller. This phenomenon is called quenching of the orbital angular momentum.⁶²⁾ Magnetic properties of matter are dictated mostly by the contribution of the spin moments.

Rotating sphere as an analogy of electron spin⁶³⁾

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An electron possesses a fundamental property called spin, and an angular momentum as well as magnetic moment associated with it. Both of these values are physical constants.⁶⁴⁾

Spin is a quantum property and does not have a direct equivalent in classical physics. However, because of the difficulty of explaining the concept, an analogy is typically used, in which an electron is portrayed as a sphere spinning around its own axis. Such spinning movement would also have a “mechanical” angular momentum associated with it.

Spin magnetic moment is also explained conceptually by the analogy of a spinning sphere. If the surface of the sphere has electric charge distributed on its surface, then as the sphere is spinning the surface electric charges rotate with it. This is equivalent to charge moving in a circular pattern which is equivalent to electric current in a loop, and therefore there would be also magnetic dipole moment associated with such a structure.⁶⁵⁾⁶⁶⁾ However, such analogy should not be used for any quantitative calculations, because the size and the distribution of charge of the electron are unknown.⁶⁷⁾

Electron's angular momentum is $L = h/(4·π)$ = 5.27 × 10^-35 J/Hz, where h is the Planck’s constant.⁶⁸⁾ The Planck constant is often used in its “reduced” version represented by the “h-bar” such that $\hbar = h/(2·π)$.⁶⁹⁾

Therefore, the angular momentum can be written as $L = \hbar/2$.⁷⁰⁾ This “divide by 2” factor denotes that the electron spin moment $m_s$ is only allowed to take two values -1/2 and +1/2 (it is quantised), typically referred to as the spin pointing “up” or “down”, respectively.⁷¹⁾

The spin magnetic moment $μ_{spin}$ is directly related to the angular momentum $m_s$ and Bohr magneton $μ_B$ such that $μ_{spin} = -g_e · μ_B · m_s $, where $g_e$ = 2.002319 (unitless constant). Therefore, $μ_{spin} \approx μ_B$.⁷²⁾

Calculation of particle momentum (and therefore spin magnetic moment) involves mass in the denominator. Therefore, the contribution of magnetic moments of protons and neutrons is mostly negligible, because of the mass being larger by more than 3 orders of magnitude that it is the case for electron.⁷³⁾

Atoms can form multi-atom molecules of chemical compounds by forming bonds. All chemical bonds are electromagnetic in nature, and they arise because of the activity of the electrons on the outermost shells.⁷⁴⁾

Atomic subshells have a preference to be fully occupied, and an atom with fully occupied outermost subshell is inert chemically (He, Ne, Ar, etc.) On the other hand, if an atom has just a single electron in the outermost shell then it is very reactive chemically (H, Li, Na, etc.) Some atoms are reactive enough that in the absence of other types of atoms they can form bonds between themselves. For example, in common air, both oxygen and nitrogen occur predominantly in diatomic configuration: O₂ and N₂.⁷⁵⁾⁷⁶⁾

Depending on the exact details energetic conditions the bonds can be broadly classified as covalent or ionic.⁷⁷⁾

Antimatter is a type of matter which has similar properties to normal matter. However, some of its property are exactly opposite, like for instance electric charge. Should a matter particle and its antimatter equivalent come in contact they will annihilate completely, producing a burst of electromagnetic radiation.

An antimatter equivalent of electron is called anti-electron or positron. It has the same mass and size, but positive electric charge, and therefore also the spin direction is reversed.

Positrons are generated in some radioactive processes. For example, unstable isotopes with shortage of neutrons decay with beta decay (β+), by emitting a positron, such that a proton becomes a neutron and the atomic number changes.⁷⁸⁾

This positron-electron annihilation process is used for example in positron emission tomography for medical diagnostic purposes. A suitable radioactive chemical (e.g. fluorine-18, half-life of just 2h) which undergoes the β+ decay is introduced into the human body, where it can be disproportionately absorbed in some abnormal tissue. The emitted positron immediately encounters normal electron (in the surrounding tissue) and they annihilate, producing two high-energy gamma photons travelling at 180° trajectories to each other. These two photons are detected and by precise timing it is possible to compute their origin, thereby allowing non-invasive 3D imaging. ⁷⁹⁾

Electrons are involved in microscopic (atom-level) phenomena which control a lot of macroscopic behaviour of materials, such as electric and magnetic properties.

Periodic table of elements, with magnetic properties⁸⁰⁾ (at very low temperatures, and also high pressure, many elements become superconducting and hence strongly diamagnetic)

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By convention, direction of electric current is opposite to the movement of electrons

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Electricity is related to the presence (electrostatics) and movement (electric current) of electric charges. The properties of electricity have been harnessed for generation, storage, transmission, and utilisation of energy, on a local and global scale.

Electric energy is based on the flow of electric charges, which is equivalent to electric current. In ordinary metal conductors the electrons are free to move, and even small electric field applied across a conductor can results in a significant current flow.⁸¹⁾

In liquids and gasses the electric field can separate electrons from atoms, thus forming positively charged ions (cations), which can also move. Such positive charges move in the same direction as the assumed convention of electric current (from plus to minus). However, metals in liquid form remain relatively good conductors, for example mercury, which is liquid at room temperature. In such metals the electrons are the main carried of electric current.

Depending on the mobility of electrons and the associated resistivity, materials can be broadly classified into four groups, significant from engineering viewpoint: insulators, semiconductors, conductors and superconductors.⁸²⁾

There are many materials and substances which can have resistivity values in-between these ranges, for various reasons (temperature, moisture content, etc.) In general, higher temperature adds energy to the system and increases quantity or mobility of electrons in insulators and semiconductors.

Resistivity of materials at room temperature spans over more than 30 orders of magnitude (superconductors have zero resistivity and cannot be represented on a logarithmic scale, but they would lie to the left of conductors)

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Electric wire engineered to have copper conductor inside, and insulator outside

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Electric insulators are all materials, in which the electrons remain bound to the atoms. Therefore, there are few free electrons to sustain the current flow. Such materials are used to insulate a given electrical conductor, so the current flows in the intended path, not leaking away in an uncontrolled way.

However, there are no perfect insulators, because some electrons are always present and will move under the applied electric field. Also, when the voltage across an insulator is increased to very large values the electrons can be ripped away from the atoms (ionisation), and gain enough energy from the electric field to cause an avalanche effect. This creates a low-resistance path and a violent discharge through the material (electric breakdown). Some of the ionised electrons return back to the atoms, releasing photons, which is the reason why an electric arc emits visible light.⁸⁴⁾

Electrical insulators typically degrade over time (their resistivity decreases by increasing mobility of electrons), especially if they remain energised. The flow of electricity through an insulator is very small but it can be measured by very sensitive devices. For example, the state of electrical insulation can be verified by using devices such us insulator resistance tester. A voltage is applied to an insulator, typically with a value equal or greater than the nominal operating voltage of the system. The small resulting current is measured and the resistance is calculated. Industrial testers can measure resistance from MΩ to tens of TΩ⁸⁵⁾, and laboratory ones even higher⁸⁶⁾.

Higher energy of the system frees up more electrons, so resistivity decreases with increasing temperature. Also, higher temperature reduces insulating properties in terms of lifetime, and around a room temperature an increase by 10°C reduces the insulation resistance (and useful life of insulation) roughly by half.⁸⁷⁾

Once a breakdown of solid insulation happens, then typically an irreversible damage occurs, for example by creating carbonised path, which serves as a low-resistance path for the electrons.

Deflection coils in a cathode-ray tube display

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Perfect vacuum itself does not conduct electricity, therefore in a theoretical sense it has infinite resistivity. However, in practice, vacuum must be contained in some matter, and therefore usual limitations apply, because sufficiently high electric field can extract electrons from atoms, and once free they will travel unimpeded through vacuum, as space current. The insulating property of vacuum is used for example in vacuum relays.

Electrons travelling in vacuum were utilised extensively in cathode-ray tube displays (CRT) in TV sets and oscilloscopes popular in XX century, as well as other vacuum tubes. Electrons were emitted from a heated cathode, and accelerated by electric field due to high voltage (typically between 10 kV and 35 kV) towards the display covered with a luminescent layer.

The position of the beam of electrons hitting the display was controlled by deflection coils, whose magnetic field was rapidly modifying the trajectory of electrons, due to Lorentz force. The luminescent layer was required to convert the energy of electrons (invisible) to the spectrum of light visible to human eye.

Modern electronics relies on semiconductors ^{Robivy64, Public domain}

In semiconducting materials the electrons require less energy to leave atoms, and their mobility can be controlled by various means, like increasing temperature, alloying with more conductive materials, applying electric field, and many more.

Technical semiconductors are sophisticated materials, whose performance is fine-tuned to specific application. For example, pure silicon is not conductive enough to be useful in its raw form. In order to obtain the required performance it is doped with other atoms, such as phosphorus (donating one extra electron, n-type) or boron (creating a shortage of one electron, called hole, p-type). Therefore, the electrical current can flow as a results of the excess of electrons, or the electrons jumping from a hole to hole, which is equivalent to the hole moving in the other direction, as if a positive charge was moving instead of a hole.⁸⁸⁾

The difference in mobility and behaviour of these electrons or electron holes is the basis for the widely useful electronics technology. The word electronics comes directly from electron.

In semiconductors typically mobility of electrons increases with increasing temperature and thus resistivity reduces accordingly. However, there are additional effects resulting from the mobility of electrons and holes, and the interaction between them, that highly non-linear effects can become more important. For example, a combination of p-type and n-type semiconductors, the p-n junction is the basis for a diode, which conducts the current in one way, and blocks in the other way. Changes in temperature of such junction just change the leakage current (in the blocking or reverse direction), or change the voltage drop across the p-n junction (in the forward or conducting direction).

The changing mobility of electrons with temperature is used in variable-resistance devices such as thermistors. Typically, they exhibit an exponential relationship: a negative temperature coefficient (NTC) means that their resistance decreases with temperature, whereas for positive (PTC) it increases.⁸⁹⁾

Physicist work on combining the magnetic and semiconducting effects, in which both the movement of electrons (electric current) and their magnetic spins are utilised. These phenomena give rise to new classes of materials, with names such as: magnetic semiconductor, diluted magnetic semiconductors and magnetic insulators. They are the subject of the science branch called spintronics⁹⁰⁾ (as an analogy to electronics).

In metals, which are good conductors, the atoms are packed so close to each other that the electrons can freely interact with other atoms. In effect, an internal electron gas⁹¹⁾ is formed and application of electric field results in a flow of electrons forming an electric current with a significant magnitude even for small applied voltage.

Inside an unenergised conductor, the electrons move freely and randomly, with very large speed of around 10⁵ m/s. Application of voltage across a conductor makes the electrons to drift towards the positive electrode, but the average drift speed is very low (e.g. 0.03 mm/s). However, due to very big number of electrons per volume (10²³ per mm³) the resulting current is still relatively high, and because all electrons drift at the same speed the current flows throughout the whole wire. The movement of electrons is due to the electric field at the surface wire.⁹²⁾

At increased temperature the atoms vibrate more vigorously and the movement of electrons is scattered more, so the resistivity of metals generally increases with increasing temperature.

The electrons can also hit the ends of the conductor and thus generate electrical noise (Johnson's noise, shot noise, etc.), which is also related to the temperature (thermal noise).

An isolated object can be charged electrostatically by depositing electric charges on its surface.

The surface of insulators can be charged by rubbing other insulating materials against them, which builds up the electrostatic charges due to triboelectric effect.

In conductors it is sufficient to touch the surface with other charged body and the charges will equalise between the two systems.⁹³⁾ But these surfaces charges (electrons) repel each other and they will tend to occupy the farthest possible distance from one another. On a hollow conductor all charges will remain only on the outer surface, leaving the inside of it with zero electric field. Similar applies even if the construction is made from a mesh, rather than solid surface. Such a conducting “cage” is known as Faraday cage and it is used widely for shielding of electric fields.

Niobium-titanium superconducting cable^{94) Copyright © CERN}

The resistivity of metals decreases with lowering temperature, because the atoms vibrate less, and therefore there is less scattering of the electron movement.

H.K. Onnes carried out experiments on mercury in 1911, and discovered that its resistivity was reducing at lower temperatures, but then vanished below 4.2 K, becoming superconducting.⁹⁵⁾ Several other materials were found to be superconducting at very low temperatures, and interestingly these materials are not the best conductors are room temperature (e.g. lead). All the superconductors operate at very low temperatures so appropriate cooling is required (liquid nitrogen or liquid helium). In 2020 it was reported that superconductivity was attained at +15°C, but at extremely high pressure, not useful for practical applications.⁹⁶⁾

In superconductors the electrons can move without electrical resistance, and without the energy loss associated with it. Therefore, in a closed superconducting loop, once a DC current is induced it can flow indefinitely (there is no energy loss), producing DC magnetic field around itself. This behaviour is used in superconducting electromagnets which can operate in persistent mode.⁹⁷⁾

For the type I superconductors (with sharp transition of critical field) the theoretical explanation is that electrons form pairs (Cooper pairs) whose movement is mediated coherently by the lattice vibrations. Understanding of the electron mobility in type II and high-temperature superconductors is still incomplete.⁹⁸⁾

Any moving charge creates magnetic field around itself (velocity field). The individual fields from each electron in a current-conducting wire overlap and create a macroscopic magnetic field around such wire.

The wires can be wound in coils or windings to shape or direct the global field in the desired manner so that operation of many devices is possible: generator, transformer, motor, sensor, antenna, etc.

Magnetic field around a moving electron (because of the convention the electron moves in the opposite direction to electric current)⁹⁹⁾

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Electric current I generates magnetic field strength H whose vector is always perpendicular to the direction of I, according to the right-hand rule

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Magnetic field lines of a solenoid (cross-section view)

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All materials respond to magnetic field to some extend, including vacuum (which is a reference point for the magnetic constant)¹⁰⁰⁾, but some with stronger interaction than others. The response is dictated by the configuration of electron spin moments in the atoms.

There are three main types of magnetic responses, or types of magnetism: ¹⁰¹⁾

• Diamagnetism - all electrons are paired in all orbitals. As a result there is no net spin moment. Application of magnetic field to such materials introduces changes to the shape of orbitals, similar to a current induced in a loop, in the direction opposing the applied field. Thus diamagnets have permeability lower than vacuum and are repelled from magnetic field. However, this effect is so small that in everyday applications they are simply classified as non-magnetic materials.
• Paramagnetism - some atoms have at least one unpaired electron, and its spin can respond to the applied field. The more the spin can be oriented with the field the larger the permeability. Paramagnets are attracted to magnetic field, but the effect is also very weak (non-magnetic).
• Ordered magnetism - the atoms have unpaired electrons and they are positioned such that they can interact with each other, which leads to spontaneous magnetisation, high permeability and strong magnetic forces (magnetic materials). Depending on the type of ordering there can be:
  • ferromagnetism
  • ferrimagnetism
  • antiferromagnetism (ordered but non-magnetic)
  • and several others.

All magnetic materials (exhibiting ordered magnetism) become paramagnetic at sufficiently high temperatures (above Curie temperature), because the thermal agitation of atoms can overcome magnetic ordering of electron spins. Conversely, paramagnets increase their permeability with lowering temperature, such that some become ferromagnetic.¹⁰²⁾

Scanning electron micrograph of a single N. meningitidis cell, with resolutions far exceeding 200 nm available from the optical microscopes ^{by Arthur Charles-Orszag, CC-BY-SA-4.0}

The resolution of ordinary microscopes is limited by the wavelengths of visible light, so objects smaller than around 200 nm cannot be resolved.¹⁰³⁾

However, using techniques such as scanning electron microscopy (SEM), the resolution can be improved by up to three orders of magnitude, so that features around 0.2 nm in size can be resolved.¹⁰⁴⁾

In SEM, a beam of electrons is generated from a heated cathode and accelerated with high voltage towards the sample. Magnetic lenses are used to focus and direct the electron beam (in some sense similar to CRT displays).

The high-energy electrons impact the sample and cause secondary electrons to be scattered - these can be detected and translated into useful information, which can be then translated into useful images.

However, there are some additional conditions which have to be met, for instance the sample must be conductive, or be prepared by applying some conductive coating (e.g. gold or palladium), and the observation is carried out in vacuum.¹⁰⁵⁾

• Proton
• Atom
• Electric charge
• Magnetic field