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A SQUID uses Josephson junctions in a loop made from a superconductor to detect changes in magnetic flux.

The magnitude of one magnetic flux unit for an electron-pair order parameter, whose electric charge has magnitude $2e$. The enclosing contour must satisfy the flux condition in fluxoid and flux quantization in a superconductor; it is not a statement that every finite area inside the material contains an integer number of these units.

An electrical transformer transfers energy between windings through electromagnetic induction. Its operation depends on changing magnetic flux, rather than a static magnetic field alone.

A transverse electric mode of a rectangular waveguide has $E_z=0$ while its axial magnetic field is generally nonzero. For time dependence $e^{-i\omega t}$ and axial dependence $e^{i\beta z}$, set $\Delta =(\omega /c{)}^2-{\beta }^2$. The Maxwell equations reconstruct the transverse components from $B_z$:The axial complex amplitude satisfies a transverse Helmholtz equation, $({\partial }_x^2+{\partial }_y^2+\Delta )B_z=0$. Zero tangential electric field at each perfect conductor wall becomes a Neumann boundary condition on $B_z$. Separation of variables givesThe index $m$ counts half-periods across $a$, and $n$ across $b$. Either index can vanish, allowing ${\mathrm{TE}}_{10}$; both cannot vanish. Indeed a spatially constant axial oscillating magnetic field would give nonzero changing magnetic flux through the cross-section, whereas the line integral of tangential electric field around its metal boundary is zero. The integral form of Faraday's law excludes this ${\mathrm{TE}}_{00}$ candidate. Dividing the reconstruction formulas by $\Delta =0$ would be invalid and cannot produce the separate transverse electromagnetic mode.

For $m=1,n=0$, choose $B_{\ast }=-i(\pi /a)E_0/\omega$. The formulas recover exactly the $E_y$, $B_x$ and $B_z$ in rectangular electromagnetic waveguide. In particular, the transverse magnetic field accompanies $B_z$ and ensures zero divergence; an oscillating longitudinal magnetic field on its own is not the guided solution.

A type-II superconductor can admit magnetic flux through quantized vortices while retaining superconductivity between their cores. Its superconducting mixed state lies between the lower critical magnetic field and upper critical magnetic field. These are equilibrium bulk distinctions; sample shape, flux pinning and preparation affect a measured magnetic response.

The motivating thin-film experiments changed an apparently minor preparation detail. Nikolay Zavaritskii evaporated metal onto glass; Alexander Shalnikov proposed cooling the substrate to helium temperatures to suppress agglomeration. The resulting critical-field behavior no longer matched the small-parameter approximation. Alexei Alexeyevich Abrikosov found a different regime within the same theory, rather than discarding its equations.^[ref]

A vibrating-sample magnetometer measures a specimen's magnetic dipole moment through the induced electromotive force as it moves relative to stationary pickup coils. Dividing that magnetic dipole moment by the specimen's independently determined volume gives its average magnetization.

In Simon Foner's 1959 apparatus, the specimen was weighed and glued to a mount. A loudspeaker drive moved it perpendicular to an applied uniform magnetic field between magnet poles; stationary coils detected the induced electromotive force. A reference magnet on the same vibrating assembly generated a second coil electromotive force. Adjusting the reference voltage divider to an electrical null compared the specimen signal with this reference. The measurement calibration substituted a magnetically saturated pure nickel sphere of known magnetic dipole moment; a specimen-removed reading corrected the mount's contribution. The calibrated signal inferred the specimen's magnetic dipole moment, not its local magnetization map. Measurement uncertainty in the standard, positioning, finite specimen size, coil noise, and mechanical coupling limited the inference.^[ref]

The readout follows Faraday's law of induction. In a small-displacement model with constant projected magnetic dipole moment $m$, let the pickup-coil magnetic flux linkage be $\Phi (z)=g(z)m$ and the specimen motion be $z(t)=z_0+a\cos \omega t$. Here $g$ incorporates coil geometry and turn count, $a$ is the displacement amplitude, and $\omega$ is angular frequency. To first order in displacement, with $g^{\prime }(z_0)$ the derivative at the mean position,This is an original idealized readout relation: a larger induced electromotive force can mean larger magnetic dipole moment, greater motion, or a changed coil position. A synchronously moving reference allows common motion factors to cancel in the ratio of induced electromotive forces. The measurement calibration and specimen-removed control are therefore integral to the measurement. A single amplitude reading cannot by itself distinguish microscopic alignment from a change in individual magnetic dipole moments.

The weber is the SI unit of magnetic flux, with $1\mathrm{Wb}=1\mathrm{T}{\mathrm{m}}^2$. A uniform magnetic field of $1\mathrm{T}$ crossing a flat surface of area $1{\mathrm{m}}^2$ along its chosen unit normal gives $1\mathrm{Wb}$. ^[ref].