A narrow population band undergoing uniform electrophoresis and ordinary diffusion has mean position $x_0+\mu Et$ and variance ${\sigma }_0^2+2Dt$. This follows from the advection-diffusion equation by changing to the coordinate $x-\mu Et$. For two species with mobility difference $\Delta \mu$, their centre separation is $|\Delta \mu |Et$, whereas diffusion widths grow only as $\sqrt{t}$. Starting from point-like bands with common diffusion coefficient $D$, a required separation of $q$ standard deviations needsA prescribed distance between centres alone is a resolution convention; finite loading widths and other dispersion mechanisms must be included when interpreting actual electrophoresis data.

An electron occupying an atomic orbital without a partner of opposite spin in that atomic orbital.

Friedrich Hund's rules describe the usual ground-term ordering within an atomic electron configuration in the LS coupling regime. First maximize the total spin $S$ subject to the Pauli exclusion principle. Among the terms with that spin, maximize total orbital angular momentum $L$. Within the resulting term, the lowest level has $J=|L-S|$ for a less-than-half-filled open subshell and $J=L+S$ for a more-than-half-filled one. These are ordering rules, not universal replacements for diagonalizing an arbitrary atomic Hamiltonian operator.

For two equivalent $p$ electrons, parallel spins give $S=1$. Their spatial wavefunction must be antisymmetric; the highest allowed orbital projection with parallel spins is $1+0=1$, giving $L=1$. A $p^2$ subshell is less than half filled, so its lowest term symbol is ${}^3{P}_0$, followed within that term by ${}^3{P}_1$ and ${}^3{P}_2$. Closed subshells contribute zero total $L$ and $S$.

A beam of electrons in a partially evacuated tube, studied in the Thomson charge-to-mass experiment.

Release of electrons from a heated material; one source of electrons in an X-ray tube.

Heating a metal gives some electrons enough energy to escape its surface. A heated diode cathode can therefore supply an electric current across a vacuum gap to a collecting diode anode. This makes temperature a control for the supply of electrons. Conversely, measuring that supply at several temperatures lets us estimate the surface work function: the energy barrier measured from the Fermi level to the nearby vacuum level. A Richardson plot turns the strong exponential function dependence into a slope.

Three questions must be kept separate: how many electrons cross the surface, how many traverse the gap, and how many the collecting diode anode records. The Richardson-Dushman law answers the first under specified surface assumptions. Space charge can obstruct the second, while incomplete collection can alter the third.

A device that produces and accelerates a directed beam of electrons.

An electron emitted from a material after excitation by incident radiation or particles.

An incident electron that returns out of the entrance side of a specimen after scattering.

The average loss of electron kinetic energy per path length, including collisional and radiative contributions.

A change of direction of an electron through interaction with matter. It can redistribute a transmitted beam outside a detector's collection region without stopping every diverted electron.

The rest mass of an electron.

A collection of mobile electrons treated statistically. A dense electron gas in a metal generally requires Fermi-Dirac statistics.

The classical electron radius is the length scale $r_e=e^2/(4\pi {ϵ}_0{m}_e{c}^2)$ formed from the elementary charge, vacuum permittivity, electron mass and speed of light. It is not a measured material radius of an electron. In the classical low-energy scattering model it sets the Thomson cross-section, ${\sigma }_T=8\pi r_e^2/3$.

Phenomena involving magnetic fields, including those produced by electric currents and magnetic moments.

A small total magnetic moment can hide extensive magnetic order. Compare three questions: are the individual magnetic moments nonzero, how are their directions correlated, and what is their vector sum? Ferromagnetism, antiferromagnetism, and ferrimagnetism answer the second question differently. The third question alone cannot identify the order.

An eddy current is a circulating electric current induced within an electrical conductor by changing magnetic flux, as described by Faraday's law of induction. Its magnetic field opposes the inducing change according to Lenz's law; electrical resistance converts electrical energy into heat.

Electromagnetic induction includes an induced electromotive force associated with a changing magnetic field or motion of a conductor in a magnetic field. Faraday's law of induction and motional electromotive force specify the relevant contributions.

Electricity concerns phenomena associated with electric charge, including electric fields and electric currents.

Electromagnetic reciprocity relates the response obtained after exchanging source and receiver in a linear reciprocal medium. For suitably normalized ports it gives a symmetric scattering matrix. It does not require zero reflection. A magnetically biased Faraday effect provides an important optical example in which reciprocity can fail.

Section 13.4; whole-book authorship applies.

Online text: web.mit.edu/course/6/6.013_book/www/chapter13/13.4.html

Cited passage: Demonstration 13.4.1 and Fig. 13.4.5.

For negligible self-inductance, a loop with electrical resistance $R$ obeys $I=-{\dot{\Phi }}_{\mathrm{ext}}/R$. With ${\Phi }_{\mathrm{ext}}=AB(t)\cos \theta$, this gives $I=-(A/R)\dot{B}\cos \theta +(A/R)B\sin \theta \dot{\theta }$. Its magnetic torque isFor $B=B_0\sin \omega t$ and slow mechanical motion, the first term averages to zero while the second gives the displayed opposing torque. A stationary loop nevertheless experiences an alternating torque at $2\omega$ and generally executes small forced motion. The zero leading mean aligning torque is not a claim of exactly zero instantaneous motion or of no higher-order effect.