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Write the magnetic flux linkage of the stationary pickup coil as $\lambda ={\sum }_{n=1}^N{\Phi }_n$, in SI units of weber. If every turn links the same magnetic flux $\Phi$, then $\lambda =N\Phi$; the turn count is dimensionless. With a fixed winding and terminal convention, Faraday's law of induction gives the induced electromotive forceThis is the fundamental theorem of calculus applied to magnetic flux linkage. Its units are $\mathrm{V}\mathrm{s}=\mathrm{Wb}$, not volts alone. Reversing the leads reverses the sign. In a high-input-electrical resistance voltage measurement the input approximately follows this electromotive force; coil loading and the frequency response of the electronics require separate calibration.

Separate direct drive linkage from material linkage: $\lambda ={\lambda }_{\mathrm{drive}}+{\lambda }_{\mathrm{material}}$. Even an empty pickup coil has $-d{\lambda }_{\mathrm{drive}}/dt$. In an ideal long, uniformly coupled specimen with negligible demagnetizing field correction and eddy current shielding, a useful material approximation isHere $A_s$ is specimen cross-sectional area, not the larger coil aperture; ${\mu }_0$ is vacuum permeability and $M$ the axial magnetization sampled by the coil. The units check directly: $(\mathrm{V}s/(\mathrm{A}\mathrm{m}))({\mathrm{m}}^2)(A/m)=\mathrm{V}\mathrm{s}$. Finite geometry and nonuniform magnetization generally require a calibrated coupling in place of ${\mu }_{0}N{A}_s$. The exact linkage identity survives that failure of the uniform approximation.

As an original illustrative calculation, stipulate $N=100$, $A_s=10^{-6}{\mathrm{m}}^2$, $\Delta M=10^{3}A/m$ and rounded ${\mu }_0=4\pi \times 10^{-7}\mathrm{V}s/(\mathrm{A}\mathrm{m})$. ThenA uniform change over $0.10\mathrm{ms}$ would give a rectangular pulse of $-1.25664\mathrm{mV}$; over $0.20\mathrm{ms}$ it gives $-0.628319\mathrm{mV}$ with the same area. Thus pulse height mixes change size with change speed. These numbers describe an ideal model, not observed pulses or material constants.

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.

An electrical transformer transfers alternating electrical power between windings through a shared changing magnetic flux. A core with large magnetic permeability confines most of the flux, so both windings link approximately the same flux $\Phi (t)$. Faraday's law gives induced electromotive forcesFor an ideal electrical transformer, negligible winding resistance and leakage flux imply the terminal-voltage magnitude ratioThe relative phase depends on the winding sense and terminal convention. At a loaded secondary, Lenz's law makes the secondary current oppose the flux change. The primary draws an additional current which approximately cancels the secondary magnetomotive force: $N_p{I}_p\simeq N_s{I}_s$ in magnitude when the magnetizing current is negligible. Consequentlyfor a resistive load, using root mean square values. More generally the ideal device conserves instantaneous power, with the appropriate current signs. A load impedance $Z_L$ appears at the primary as $Z_{\mathrm{in}}=(N_p/N_s{)}^2{Z}_L$, enabling impedance matching and electrical isolation.

For sinusoidal flux, $\Phi ={\Phi }_{\max }\sin \omega t$ gives $V_{\mathrm{rms}}=\omega N{\Phi }_{\max }/\sqrt{2}$. At a given supply voltage, reducing frequency increases the required peak flux and can drive the core into magnetic saturation. Real losses include winding Joule heating, magnetic hysteresis, eddy currents and leakage flux; a laminated core suppresses eddy-current loops. A steady direct current produces no continuing secondary electromotive force, while its small winding resistance can allow a damaging primary current after switching transients.

In the 1982 experiment, separate drives using piezoelectricity scanned a metal tip laterally and adjusted its height. A control unit held electric current fixed at constant tip-sample electric potential difference; calibrated drive voltages supplied the displacement readout. Their Fig. 1 explicitly contrasts a surface step with apparent height from contamination changing the work function.^[ref]

Gerd Binnig and Heinrich Rohrer describe a later vibration isolation system using two spring stages and eddy current damping inside a vacuum chamber, with sputtering and annealing for surface preparation. These measures addressed unwanted motion and surface condition separately.^[ref]