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The weak neutral current couples the Z boson to a fermion without changing its electric charge. Its vector and axial-vector coefficients depend on weak isospin, electric charge, and the weak mixing angle.

The neutral current transfers no electric charge at a fermion vertex; “neutral” does not mean that every participating particle is uncharged. For example, ${\nu }_{\mu }{e}^{-}\to {\nu }_{\mu }{e}^{-}$ transfers energy and momentum to an electron through Z boson exchange. By contrast, a charged current can convert a muon neutrino into a muon, as in ${\nu }_{\mu }n\to {\mu }^{-}p$. Both processes conserve total electric charge. A photon also carries no electric charge, but an active neutrino has no electromagnetic charge coupling: its neutral current is a distinct weak interaction.

The experimentally useful contrast on a nucleon target iswhere $N$ is a nucleon and $X$ is an allowed final state of hadrons. The charged current makes a charged lepton available for identification; the outgoing neutrino in a neutral current leaves no bubble-chamber track. A sample of hadronic events without an identified muon therefore poses an experimental question: how many could instead be neutron interactions, or charged current events whose muon was missed? The answer requires a detector-response and background analysis, not merely an inspection for an absent line.

A particle with zero net electric charge.

The neutron is the electrically neutral spin-one-half baryon found with protons in most atomic nuclei.

A neutron is a nucleon: it contributes to an atomic nucleus without adding electric charge. Its spin one-half makes it a fermion, and it belongs to the baryons. Electrical neutrality does not mean an absence of interactions: a neutron can transfer momentum and kinetic energy to an atomic nucleus, producing a charged nuclear recoil that a particle detector can register. This indirect route is central to neutron detection by proton recoil.

The beautiful feature of the Chadwick neutron discovery experiment is that an unseen projectile acquired a measurable mass through the motion of things it struck. Penetration alone left competing explanations open; combining nuclear recoils from different target masses supplied a much stronger test.

The nitrate ion, ${\mathrm{NO}}_3^{-}$, is an anion with one nitrogen connected to three oxygen chemical atoms and net electric charge $-1$ in units of elementary charge. Its 24 valence electrons admit three equivalent octet resonance structures; see Lewis structure for their construction and chemical resonance for their interpretation. The N–O connections are covalent bonds within the ion. See 7.2 Covalent Bonding.

For the global phase symmetry of a complex scalar field oriented as $\delta \psi =-i\epsilon \psi$, the Noether current is $j^{\mu }=i({\psi }^{\ast }{\partial }^{\mu }\psi -\psi {\partial }^{\mu }{\psi }^{\ast })$. The Euler-Lagrange field equations $\square \psi +V^{\prime }(|\psi {|}^2)\psi =0$ and its complex conjugate give ${\partial }_{\mu }{j}^{\mu }=i({\psi }^{\ast }\square \psi -\psi \square {\psi }^{\ast })=0$ for a real differentiable potential. Integrating $j^0$ gives $Q$ when boundary flux vanishes. A charged scalar coupled to electromagnetism has electric charge $qQ$ with the chosen charge normalization; without that physical identification it is an internal charge.

For $D_{\mu }={\partial }_{\mu }+iq{A}_{\mu }$, the constant phase transformation $\delta \varphi =-iqϵ\varphi$ has the displayed Noether current. Varying the gauge field gives ${\partial }_{\mu }{F}^{\mu \nu }=J^{\nu }$. In this convention $J^{\mu }=iq({\varphi }^{\ast }{\partial }^{\mu }\varphi -\varphi {\partial }^{\mu }{\varphi }^{\ast })-2q^2{A}^{\mu }|\varphi {|}^2$. The matter equations imply ${\partial }_{\mu }{J}^{\mu }=0$; the integrated electric charge additionally requires zero boundary flux. Local phase invariance gives a Noether second theorem identity, rather than independent physical charges for arbitrary functions.^[ref]

A nonelectrolyte supplies neutral molecules rather than ions on dissolving in the specified solvent, as illustrated by sucrose in water.

For example, dissolving an idealized $1\mathrm{mmol}$ sucrose inventory gives $1\mathrm{mmol}$ dissolved sucrose molecules, rather than separate cations and anions. Dissolving the same amount of substance of a fully dissociated one-to-one strong electrolyte instead gives $1\mathrm{mmol}$ of each ion. Both can disappear visibly into the solvent; the resulting chemical species distinguish them.^[ref]

A nonelectrolyte is not necessarily insoluble: sucrose provides a soluble counterexample. Nor does the label assert exactly zero measured electrical conductivity. Self-ionization of water, impurities or residual electrolyte from a probe can supply background ions. Comparing with a solvent blank and rinsing between samples, as in the strong electrolyte experiment, tests whether the dissolved substance itself produces appreciable additional mobile ions. This separates visible dissolution from ion production without treating lamp darkness as an absolute absence of electric charge.

An n-type semiconductor has more mobile electrons than electron holes. The letter describes the predominant mobile charge carriers, not a net negative electric charge of the whole material.

A spatial charge density describing the electric charge inside an atomic nucleus. In a static description centered on the nucleus, normalize it bywhere $Z$ is the atomic number and $e>0$ the elementary charge. A nuclear charge distribution is an average over a nuclear quantum state, rather than a photograph of immobile protons. Even when the average has spherical symmetry, individual nucleons need not sit on spherical shells. The proton charge radius and the internal charge density of the neutron also contribute: a distribution of pointlike proton centers is an approximation to a nuclear charge distribution, not its definition.

The experimental attraction is that an electron probes electric charge through the electromagnetic interaction, without itself feeling the nuclear force. Varying its momentum transfer changes the spatial scale tested. Long wavelengths mainly constrain a nuclear charge radius; shorter wavelengths can distinguish a diffuse edge from a sharper one through diffraction. Recovering the entire nuclear charge distribution from a finite range of noisy scattering data remains an inverse problem.

In the static charge density model, define the normalized Fourier transformHere $\mathbf{q}=(\mathbf{p}-{\mathbf{p}}^{\prime })/\hslash$ is the spatial momentum transfer divided by the reduced Planck constant: $q=|\mathbf{q}|$ has units of inverse length. Physical momentum transfer is $\hslash \mathbf{q}$. We keep $\hslash$ and the speed of light $c$ explicit; compute $q=|\mathbf{p}-{\mathbf{p}}^{\prime }|c/(\hslash c)$, expressing the numerator in $\mathrm{MeV}$ and $\hslash c$ in $\mathrm{MeV}\mathrm{fm}$, to obtain $q$ in inverse femtometres. The spatial $q$ is distinct from the invariant four-momentum transfer used in relativistic scattering cross-sections.

For spherical symmetry, take the polar axis along $\mathbf{q}$ and use spherical coordinates. With $\mu$ the cosine of the polar angle,Every radial shell contributes an amplitude. At $q=0$ all shells add with the same sign; at larger $q$ their contributions can cancel. This cancellation is the origin of a diffraction minimum in the nuclear charge form factor, rather than an absence of electric charge in the nucleus.

The static Fourier transform interpretation is appropriate for the nuclear model and kinematic regime specified here. A fully relativistic composite system requires frame and current conventions; its electric form factor is not universally the transform of a frame-independent three-dimensional charge density.

Robert Andrews Millikan's 1911 protocol alternated electrically driven ascent with timed descent after short-circuiting the plates; a changed ascent speed signalled ion capture.^[ref]

His 1913 refinements checked voltage before and after runs, calibrated optical distance and the clock, compared independent air-dynamic viscosity measurements, and varied pressure to test slip.^[ref] His 1924 lecture describes suppressing convection, switching the electric field, neutralizing drops, and reproducing smallest observed electrical speed increments.^[ref]

Harvey Fletcher's posthumous account recalls building the first oil apparatus and measuring with Robert Andrews Millikan; priority for suggesting oil remains uncertain.^[ref]

To interpret the readout, keep one drop and one electric field polarity. Let $u_i$ be its signed upward terminal velocity in charge state $i$, and let $v_f>0$ be its field-off falling speed. Use the linear drag coefficient $k$ already defined in elementary charge, with any required gas slip correction to Stokes drag included. Provided the drop's radius, surrounding air and electric field remain fixed, its electrical speed increment isThese relations apply while the electric force points upward in every state. A drop may still descend, with $u_i<0$, when that force is too weak to support it. A held drop has $u_i=0$ and therefore $S_i=v_f$, rather than zero electrical response. A neutral drop has $S_i=0$: its signed terminal velocity agrees with field-off descent. Thus neither raw upward speed nor the ability to hold a drop is itself a count of electrons.

The ratios cancel a fixed $k/E$, even if its value is poorly known. This is why relative charge quantization and absolute measurement calibration are different questions. A changed field-off $v_f$ warns that evaporation, air motion or another change has spoiled comparison of charge states. A stable $v_f$ is useful evidence but cannot exclude every compensating change. Repeat field-off checks around a proposed jump, allow the terminal velocity under linear drag to settle after switching, and propagate measurement uncertainty in both the field-on and field-off readings. Reusing a single estimate of $v_f$ gives the different $S_i$ a shared covariance.

The oil drop experiment infers an oil drop's electric charge from its motion under gravity, buoyancy, drag and a calibrated electric field. Repeated changes of a single drop's electric charge reveal discrete steps; see the model, experimental procedure and limitations in elementary charge.

The 1964 report exposed Brookhaven's 80-inch hydrogen bubble chamber to a mass-separated $5.0\mathrm{GeV}/c$ negative-kaon beam. A photographed decay chain, track momenta and bubble density supported the particle identification. Two converted photons helped reconstruct a neutral pion. Alternative assignments were tested kinematically. The authors reported an Omega baryon candidate with $Q=-1$, $S=-3$ and mass $1686\pm 12\mathrm{MeV}/c^2$, reserving a detailed systematic-error discussion for further events.^[ref]

This is an inference from several linked observations. A charged particle can leave a visible bubble-chamber track, while a neutral segment must be reconstructed from its production and decay products. Agreement between possible decay channels, electric charge, momentum conservation and the reconstructed mass is stronger evidence than a suggestive track shape alone. The event tests a predicted hadron pattern; it does not photograph the three strange quarks individually.

For example, an independently constructed two-body kinematic check usesIn a parent rest frame with equal and opposite daughter momenta, the momentum sum vanishes, giving $M{c}^2=E_1+E_2$. In units $c=1$, stipulated daughter masses $m_1=1$, $m_2=1/4$ and momentum magnitude $p=3/4$ give $E_1=5/4$, $E_2=\sqrt{10}/4$ and $M=(5+\sqrt{10})/4\simeq 2.04057$. A common Lorentz boost changes the daughter energies and momenta while preserving this reconstructed invariant mass. These chosen units and numbers are an illustration, not a reanalysis of the 1964 event.

An overdamped RLC response is a free series RLC circuit response with $R>2\sqrt{L/C}$, equivalently $\alpha >{\omega }_0$. Put $\beta =\sqrt{{\alpha }^2-{\omega }_0^2}$. The distinct negative characteristic roots are $r_{\pm }=-\alpha \pm \beta$, so the general electric charge isFor initial conditions $q(0)=q_0$, $i(0)=0$,For $q_0>0$, this electric charge decreases to zero without reversing sign. In the dimensionless example ${\omega }_0=1$, $\alpha =2$, the characteristic roots are $-2\pm \sqrt{3}\approx -0.268,-3.732$. The slow term dominates late times. Stronger damping can therefore make the final return slower: for $\alpha \gg {\omega }_0$, $r_{+}\sim -{\omega }_0^2/(2\alpha )=-1/(RC)$. Nonoscillation alone does not imply a fast response, and monotonicity here uses the specified initial conditions.

An oxidation state is an electron-bookkeeping assignment to a chemical atom: its electric charge number after the ionic approximation of bonds. It helps identify oxidation and reduction and determine stoichiometry, even for covalent bonds without separate charged ions. In water, each hydrogen has oxidation state $+1$ and oxygen has $-2$; this does not assert that a water molecule contains two free protons and a free oxide ion.^[ref]

Three conventions answer different questions. Formal charge divides each bonding electron pair equally in a chosen Lewis structure. Oxidation state uses the ionic approximation of bonds. Partial atomic charge instead partitions the actual electron density and depends on that partition. In the ordinary water Lewis structure, every formal charge is zero although the oxidation states are not. Neither bookkeeping convention supplies numerical partial atomic charges.

Sum oxidation states over all chemical atoms of the specified molecule, ion or formula unit, including multiplicities:Here $q$ is the net electric charge and $e$ the positive elementary charge. For a neutral entity the sum is zero; for an ion it equals its signed electric charge number $z$. The reason is simple: the allocation assigns every valence electron exactly once, so the sum is the neutral electron budget minus the actual electron count.

For water, $2(+1)+(-2)=0$; for hydrogen peroxide, $2(+1)+2(-1)=0$. In permanganate, ${\mathrm{MnO}}_4^{-}$, assigning each oxygen $-2$ gives $x+4(-2)=-1$, so manganese has oxidation state $+7$. This is not a free ${\mathrm{Mn}}^{7+}$ ion: the entire permanganate anion has net electric charge $-e$. The sum rule supplies a constraint; without additional assignments it cannot determine every individual oxidation state.

Two broad perfect conductors of width $w$, separated by gap $d\ll w$, carry opposite steady electric currents $I$ and connect through a terminating resistor $R$. Away from edges, Ampère's circuital law and the superposition principle give gap magnetic field magnitude ${\mu }_{0}I/w$. Each conductor is an equipotential, and Ohm's law sets their electric potential difference to $IR$. Planar symmetry and charge-free Gauss's law then give uniform gap electric field magnitude $IR/d$. Injection parallel to the upper current makes the electric and magnetic Lorentz forces opposite. Their cancellation selects speed $Rw/({\mu }_{0}d)$ independent of nonzero electric charge and of operating current; nonrelativistic kinetic energy is $m[Rw/({\mu }_{0}d){]}^2/2$.

A parallel-plate capacitor consists of two parallel electrical conductors with overlapping area $A$ and separation $d$. If the gap is small compared with both plate widths and is filled by a uniform material of positive permittivity $ϵ$, its capacitance is approximatelyThis neglects the fringing field of a capacitor near the plate edges. The interior electric field points from the plate of positive electric charge to the plate of negative electric charge, and is approximately uniform. ^[ref].

For a worked vacuum example, stipulate $A=0.01{\mathrm{m}}^2$, $d=0.001\mathrm{m}$, and vacuum permittivity ${ϵ}_0\approx 8.854\times 10^{-12}F/m$. This rounds the value in Fundamental Physical Constants — Complete Listing by National Institute of Standards and Technology and others. Within the approximation,At terminal electric potential difference $V=10\mathrm{V}$, the electric field magnitude is $E\simeq V/d=10^{4}V/m$, the plate electric charge magnitude is $Q=CV=0.8854\mathrm{nC}$, and the capacitor energy is $U=C{V}^2/2=4.427\mathrm{nJ}$. These numbers use the stipulated rounded vacuum permittivity; finite plates also have corrections from the fringing field of a capacitor.

The formula makes design changes easy to predict: doubling the overlapping area doubles the capacitance, and halving the gap doubles the capacitance, with permittivity fixed and the fringing field of a capacitor neglected. Doubling permittivity also doubles capacitance if the material uniformly fills the gap and remains linear. This lets a compact device store more separated electric charge at the same terminal electric potential difference.

The short derivation uses surface charge density $\sigma =Q/A$. In the interior, Gauss's law gives electric field magnitude $E\simeq \sigma /ϵ=Q/(ϵA)$. The electric potential difference is $V\simeq Ed=Qd/(ϵA)$, so dividing $Q$ by $V$ gives $C\simeq ϵA/d$. A narrow curved capacitor gap has the same leading local approximation when its width is much less than the curvature radius.

A partial atomic charge assigns an electric charge to a chemical atom by partitioning the actual electron density. The result depends on the partitioning convention and need not be an integer. It differs from formal charge, which divides bonding electrons equally in a specified Lewis structure.

A particle accelerator increases the kinetic energy of charged particles through the work of an electric field. A single electric potential difference $V$ gives an energy gain of magnitude $|q|V$ to a particle of electric charge $q$ crossing in the accelerating direction. Reusing a smaller electric potential difference many times can give a much larger final kinetic energy without requiring the whole apparatus to withstand the equivalent single voltage. A magnetic field can return the particles to the accelerating region: magnetic forces do no work, but they make repeated energy gains possible. The cyclotron turns this separation between bending and acceleration into a particularly elegant machine.