In short

If a magnetic flux through a closed loop changes with time, an electromotive force (EMF) appears around the loop — no battery required. The relation is quantitative and is called Faraday's law:

\boxed{\;\varepsilon \;=\; -\,\frac{d\Phi_B}{dt}\;}

Here \Phi_B = \int \vec{B}\cdot d\vec{A} is the magnetic flux through the loop (for a uniform field through a flat area, \Phi_B = BA\cos\theta, SI unit weber = T·m²). The negative sign encodes Lenz's law — the induced EMF opposes the change in flux — and is explored separately in Lenz's Law.

Three ways to change flux:

  1. Change the magnitude B of the field through a fixed loop (switch an electromagnet on/off, move a bar magnet toward a coil).
  2. Change the area A of the loop inside a fixed field (a sliding rod on rails, a coil squeezed between magnet poles).
  3. Change the orientation \theta between the loop normal and the field (spin a coil in a fixed field — this is how every generator in India works).

For a coil with N turns, each turn sees the same flux \Phi_B, so the total induced EMF is

\boxed{\;\varepsilon \;=\; -\,N\,\frac{d\Phi_B}{dt}\;}

Why it matters. Every kilowatt-hour of electricity you have ever used — from the NTPC Singrauli coal plant, the Tehri hydroelectric dam, the Kudankulam nuclear station, the wind farms of Tamil Nadu, the rooftop solar charge controller in your uncle's flat — has been generated, transformed, or regulated using Faraday's law. Induction sensors on ISRO rockets, the coil of every Indian Railways regenerative-braking system, the wireless chargers in your phone, and the MRI scanner at AIIMS all work because a changing flux produces an EMF.

In 1831, a bookbinder-turned-experimentalist named Michael Faraday had a coil of wire connected to a galvanometer and another coil connected to a battery. He switched the battery on. For a moment — just an instant — the galvanometer needle jumped. Then it settled back to zero. He switched the battery off. The galvanometer needle jumped the other way, then settled again. With a steady current in the first coil, nothing happened. Only when the current was changing did the second coil see anything. That single observation, that the change mattered and not the steady state, is the entire industrial revolution of electricity.

Today you can reproduce the experiment with ₹200 worth of wire, a small bar magnet from a school science kit, and a cheap multimeter. Wrap 50 turns of enamelled copper wire around a pencil, connect the two ends to the multimeter on its millivolt setting, and shove a magnet into the coil. The display jumps to 5 or 10 mV for the instant of the push, then returns to zero. Pull the magnet out — the needle jumps the other way. Hold it still inside the coil — nothing. What Faraday discovered is as easy to see today as it was in his laboratory, and it is the single most technologically important law in physics.

Magnetic flux — what changes when we talk about "change"

Before we can write "the rate of change of flux", we need to be crisp about what flux is. The magnetic flux through a surface is a scalar that measures how many field lines pierce through it. For a uniform field \vec{B} and a flat area \vec{A} (the area vector, magnitude equal to the area, direction normal to the surface):

\Phi_B \;=\; \vec{B}\cdot\vec{A} \;=\; BA\cos\theta

where \theta is the angle between \vec{B} and the normal to the surface. For a general curved surface in a non-uniform field, you integrate over little patches:

\Phi_B \;=\; \int_S \vec{B}\cdot d\vec{A}

Why: \vec{B}\cdot d\vec{A} is the flux through a tiny flat patch; you add them up. If the loop is flat and the field is uniform, the integral is trivially BA\cos\theta.

The SI unit of flux is the weber (Wb): 1 Wb = 1 T·m² = 1 V·s. The last equivalence is a direct consequence of Faraday's law — the EMF in volts equals webers per second.

The flux is signed — you have to pick a direction

A closed loop has two possible normal directions (the two sides of the loop). Pick one. This fixes the sign of \Phi_B and the sign of the induced EMF. The convention is the right-hand rule: if you curl the fingers of your right hand along the positive direction of circulation around the loop, your thumb points along the positive normal. Reverse the direction of circulation and you reverse the sign of both \Phi_B and \varepsilon.

You never have to worry about the sign in isolation — what matters is that, once you pick a sign convention, Lenz's law (the minus sign in Faraday's law) correctly predicts the direction of the induced current.

The three ways to change flux

From \Phi_B = BA\cos\theta, there are exactly three ways to change \Phi_B — change B, change A, or change \theta. Each one is the physics behind a specific class of everyday machines.

Way 1 — change B (the magnet-and-coil experiment)

Hold a coil still. Move a bar magnet toward it. The B at the coil location grows; the flux through the coil grows; an EMF is induced. Pull the magnet away. The flux shrinks; an EMF is induced, the other way.

This is the mechanism behind:

Way 2 — change A (the sliding rod on rails)

Put two parallel horizontal rails a distance \ell apart, in a uniform vertical magnetic field \vec{B}. Lay a conducting rod across them, perpendicular to the rails, and push the rod along them at velocity v. The loop (two rails, the moving rod, and a fixed connecting wire at the other end) grows in area at rate dA/dt = \ell v. The flux through it grows at d\Phi_B/dt = B\ell v, and a motional EMF \varepsilon = B\ell v is induced. This case is so important it gets its own chapter — see Motional EMF.

Way 3 — change \theta (the rotating coil, i.e. every generator)

Put a flat coil of area A in a uniform field \vec{B}, and rotate the coil about an axis perpendicular to \vec{B} with angular frequency \omega. The angle between the loop normal and \vec{B} is \theta(t) = \omega t, so

\Phi_B(t) \;=\; BA\cos(\omega t)
\varepsilon(t) \;=\; -\frac{d\Phi_B}{dt} \;=\; NBA\omega\sin(\omega t)

(including a factor of N for N turns). The EMF is a sine wave of amplitude NBA\omega at angular frequency \omega. This is the basic physics of a generator, covered in detail in Motional EMF.

Deriving Faraday's law — from a bar magnet to \varepsilon = -d\Phi/dt

Faraday's law is one of the four Maxwell equations and, strictly, it is taken as fundamental — an empirical law that cannot be derived from simpler statements. But we can motivate it from two pieces of physics you have already seen, and in the process see where every term comes from.

The plan: start with a rod moving on rails in a field (a purely magnetic setup — no time-varying field, just a sliding conductor). Use the Lorentz force \vec{F} = q\vec{v}\times\vec{B} on the charges in the rod to compute the EMF. Show that the answer can be rewritten as -d\Phi_B/dt. Then assert that this form of the law — the flux form — is the correct one even for situations where the flux changes by a changing \vec{B} (not a moving rod). This last step is an experimental fact, not a logical deduction; it is what Faraday discovered.

Step 1. A rod of length \ell slides on frictionless rails at speed v in a vertical field \vec{B} pointing into the page (see the figure below). Pick the loop normal along +\hat{z} (out of the page). Then the flux through the loop is negative: \Phi_B = -B\cdot A, and growing in magnitude because A is growing.

Rod sliding on rails in a uniform magnetic field — flux derivation Two horizontal rails separated by distance l. A conducting rod stands vertically between them, perpendicular, moving to the right at velocity v. A uniform magnetic field B points into the page (shown as a grid of crosses). The enclosed area grows as the rod moves right. B (into page) rail rail rod, length ℓ v ℓ dA = ℓ v dt R
A rod of length $\ell$ slides on rails at speed $v$ in a field $\vec{B}$ into the page. In time $dt$, the enclosed area grows by $dA = \ell v\,dt$ and the flux magnitude by $d\Phi_B = B\ell v\,dt$. The induced EMF is $\varepsilon = d\Phi_B/dt = B\ell v$.

Step 2. The free electrons inside the rod are moving along with it at velocity \vec{v}. Each electron feels a magnetic force \vec{F} = q\vec{v}\times\vec{B} — for an electron with q = -e, this points along the rod (let's say from the top end to the bottom end). The force per unit charge is therefore \vec{v}\times\vec{B}, with magnitude vB.

Why: this is just the Lorentz force on moving charges, which you met in force on a moving charge. The magnetic field does not act on a stationary charge, but once the charges are moving with the rod they feel a sideways push.

Step 3. The EMF around a loop is defined as the work done per unit charge in carrying a test charge once around the loop. For the slide-rod geometry, the only non-zero contribution comes from the rod (the rails are parallel to \vec{v}, so the force is perpendicular to the rail direction and does no work along it). The work per unit charge along the rod is (vB)\ell:

\varepsilon \;=\; \oint \frac{\vec{F}}{q}\cdot d\vec{\ell} \;=\; (vB)\,\ell \;=\; B\ell v

Why: \varepsilon is defined as \oint \vec{f}\cdot d\vec{\ell} where \vec{f} is the non-electrostatic force per unit charge. For a moving rod, that force is \vec{v}\times\vec{B}, which is zero along the rails and equal to vB along the rod.

Step 4. Meanwhile the flux through the loop changes. In time dt the rod moves by v\,dt, sweeping out area dA = \ell v\,dt. Since \vec{B} is into the page and we chose normal out of the page, \Phi_B is more negative by B\,dA = B\ell v\,dt, so

\frac{d\Phi_B}{dt} \;=\; -B\ell v

and

-\frac{d\Phi_B}{dt} \;=\; +B\ell v \;=\; \varepsilon

This is Faraday's law for the motional case. We derived it straight from the Lorentz force.

Step 5 (the Faraday leap). Now imagine instead that the rod is stationary but \vec{B} is changing. The Lorentz force argument fails — there is no velocity. Yet experimentally the EMF is still \varepsilon = -d\Phi_B/dt. This is the central empirical fact Faraday discovered: the flux-rate formula works in both cases. Mathematically it is the statement that a changing magnetic field produces a non-conservative electric field — an electric field whose closed-loop integral is non-zero even with no charges present. Writing this out:

\oint_C \vec{E}\cdot d\vec{\ell} \;=\; -\frac{d}{dt}\int_S \vec{B}\cdot d\vec{A}

This is the Maxwell-Faraday equation, one of the four Maxwell equations, and it is taken as a law of physics on experimental grounds. Everything downstream — radio waves, light, transformers, generators — follows from it.

Interactive — bar magnet approaching a coil

The most classic Faraday demonstration is a magnet pushed into a coil. The animation below lets you drive a sinusoidal position of a bar magnet along the axis of a 100-turn coil and shows the flux through the coil (proportional to the magnet's instantaneous field at the coil centre) alongside the instantaneous EMF it induces. Because \varepsilon \propto -d\Phi/dt, the EMF peaks when the flux is changing fastest, not when it is largest.

Animated: flux and EMF as a bar magnet oscillates near a coil A horizontal axis shows time from 0 to 6 seconds. A red curve traces the magnetic flux Phi(t) = cos(t) through the coil, and a dark curve traces the induced EMF epsilon(t) = sin(t), which is 90 degrees out of phase — peaking when Phi crosses zero and zero when Phi is at its extremes. time (seconds) Φ and ε (normalised) +1 −1 1 2 3 4 5 6
As the magnet oscillates, the flux $\Phi_B(t) = \Phi_0\cos(\omega t)$ through the coil traces a cosine (red). The induced EMF $\varepsilon(t) = \omega\Phi_0\sin(\omega t)$ traces a sine (dark) — it is zero when $\Phi$ is at its peak or trough (not changing), and maximum when $\Phi$ crosses zero (changing fastest). Click replay to watch again.

The key pedagogical insight: the EMF peaks when the rate of change of flux peaks, not when the flux itself peaks. Students often think "more flux = more EMF"; the figure shows the opposite — at the instant the flux is at its maximum, it is not changing, and the EMF is zero.

Worked examples

Example 1: The dropped magnet through a solenoid

A cylindrical neodymium magnet (\Phi_B peak = 2.0 × 10⁻⁴ Wb at the coil's mid-plane) falls from rest through a 200-turn coil of negligible thickness, mounted horizontally. It enters the coil at t = 0, reaches the mid-plane at t = 0.08 s, and exits at t = 0.16 s. Model the flux through the coil as \Phi_B(t) = \Phi_0\sin(\pi t/T) for 0 \le t \le T, with T = 0.16 s. Compute the peak EMF and the instant at which it occurs.

Bar magnet falling through a coil, and the resulting flux-vs-time curve Left: a vertical stack showing a cylindrical magnet above, inside, and below a horizontal coil at three moments. Right: a plot of flux Phi(t) versus time t, a half-sine bump from t=0 to t=T. coil, N = 200 t = 0 t = T/2 (mid-plane) t = T Φ t T T/2 Φ = Φ₀ sin(πt/T) (idealised model)
As the magnet falls through the coil, the flux rises, peaks at the mid-plane, and falls back to zero. The peak EMF occurs at the moments of entry and exit — where the flux is changing fastest — and is zero at the mid-plane, where $d\Phi/dt = 0$.

Step 1. Write the flux as a function of time and differentiate.

\Phi_B(t) \;=\; \Phi_0\sin\!\left(\frac{\pi t}{T}\right)
\frac{d\Phi_B}{dt} \;=\; \Phi_0\cdot\frac{\pi}{T}\cos\!\left(\frac{\pi t}{T}\right)

Why: chain rule on \sin. The derivative is \cos multiplied by the derivative of the argument, which is \pi/T.

Step 2. Apply Faraday's law with N turns.

\varepsilon(t) \;=\; -N\frac{d\Phi_B}{dt} \;=\; -N\Phi_0\cdot\frac{\pi}{T}\cos\!\left(\frac{\pi t}{T}\right)

Step 3. Peak EMF. The cosine is at most 1 (at t = 0) and at least -1 (at t = T); in magnitude the peak is

|\varepsilon|_\text{peak} \;=\; \frac{N\pi\Phi_0}{T} \;=\; \frac{(200)(\pi)(2\times 10^{-4})}{0.16} \;=\; \frac{0.1257}{0.16} \;=\; 0.785\text{ V}

Why: pulling the \pi/T factor out gives a clean expression. Numerator is N\pi\Phi_0 \approx 0.126 Wb; divided by T in seconds gives volts.

Step 4. Timing of the peak. The cosine is 1 at t = 0 and -1 at t = T — so the EMF peaks as the magnet enters the coil and again (opposite sign) as it exits. At the mid-plane (t = T/2), \cos(\pi/2) = 0, so \varepsilon = 0 momentarily — exactly when the flux is at its peak.

Result. Peak EMF \approx 0.79 V, occurring at t = 0 and t = T = 0.16 s.

What this shows. A small neodymium magnet dropping through a 200-turn coil generates nearly a volt — easily visible on a cheap multimeter. This is the basis of the shake-torch (no batteries, just a magnet sliding in a coil), the seismometer used in Uttarakhand landslide-warning stations, and countless induction sensors on ISRO launch vehicles.

Example 2: A single-loop electromagnet switch-on

A circular coil of radius r = 8 cm sits coaxially inside a long solenoid (also along the axis, so the coil's normal is along the solenoid axis). The solenoid has 1000 turns/m and carries a current that ramps linearly from 0 to 5.0 A in 20 ms when the switch is closed. The coil has 40 turns. What peak EMF appears across the coil during the ramp?

Small coil inside a long solenoid as the solenoid current ramps up A long solenoid drawn as a rectangular outline with turns. Inside it, coaxial with its axis, sits a smaller circular coil. A plot to the right shows the solenoid current I ramping linearly from 0 to 5 A over 20 ms. long solenoid, n = 1000 turns/m coil, N = 40, r = 8 cm I (A) t 5 20 ms dI/dt = 250 A/s
A small coil inside a long solenoid. When the solenoid current ramps, the $\vec{B}$ inside it ramps too, which changes the flux through the inner coil and induces an EMF across its terminals.

Step 1. Field inside the solenoid. From Ampere's law (or the magnetic field of common current configurations):

B \;=\; \mu_0 n I

where n = 1000 turns/m is the turn density. As I(t) ramps, B(t) = \mu_0 n I(t) ramps proportionally.

Step 2. Flux through the inner coil. The coil's area is A = \pi r^2 = \pi(0.08)^2 = 0.02011 m². Because the coil is coaxial with the solenoid, the normal is parallel to \vec{B}, so \cos\theta = 1:

\Phi_B(t) \;=\; B(t)\cdot A \;=\; \mu_0 n I(t)\cdot A

Step 3. Differentiate.

\frac{d\Phi_B}{dt} \;=\; \mu_0 n A\,\frac{dI}{dt}

Step 4. Apply Faraday's law with N = 40 turns in the inner coil.

|\varepsilon| \;=\; N\mu_0 n A\,\frac{dI}{dt}

Step 5. Plug numbers. \mu_0 = 4\pi\times 10^{-7} T·m/A, n = 1000 m⁻¹, A = 0.02011 m², dI/dt = 5/0.020 = 250 A/s, N = 40.

|\varepsilon| \;=\; (40)(4\pi\times 10^{-7})(1000)(0.02011)(250)
= (40)(1.257\times 10^{-3})(0.02011)(250)
= (40)(1.257\times 10^{-3})(5.028)
= (40)(6.32\times 10^{-3}) \;=\; 0.253\text{ V}

Why: tracking units — Wb/s = V, so (T)(m^2)(1/s) = V indeed.

Result. Peak EMF across the inner coil during the ramp is approximately 0.25 V (constant during the linear ramp, zero once I stops changing).

What this shows. Coupling between two coils — a changing current in one induces an EMF in the other — is the principle behind every transformer. Doubling the number of turns N in the secondary coil doubles the induced EMF. Doubling the rate dI/dt also doubles it. This example is a tabletop preview of mutual inductance.

Example 3: A generator coil in the NTPC turbine hall

A 200-turn rectangular coil of area 0.05 m² is rotated at 3000 rpm between the poles of a magnet that produces a uniform B = 0.6 T inside the gap. Find the peak EMF and the RMS EMF induced in the coil.

Rotating coil between magnet poles — schematic of an AC generator A pair of magnet poles (N on left, S on right) produce a horizontal magnetic field. Between them, a rectangular coil is rotating about a vertical axis, so that the angle between its normal and B changes with time. N S ω axis N = 200, A = 0.05 m², ω = 2π·50 rad/s
A rotating coil in a uniform field is the heart of every AC generator. The induced EMF is a pure sinusoid of amplitude $\varepsilon_0 = NBA\omega$ at the rotation frequency $\omega/(2\pi)$ — in this case, exactly 50 Hz, the frequency of the Indian grid.

Step 1. Convert rpm to angular frequency. 3000 rpm means 3000/60 = 50 rev/s, and

\omega \;=\; 2\pi\times 50 \;=\; 314.16\text{ rad/s}

Why: 2\pi radians per revolution; multiply by rev/s to get rad/s. 3000 rpm corresponds exactly to the 50 Hz frequency of the Indian grid — this is not coincidence; generators in Indian power plants are built to spin at precisely this speed.

Step 2. Peak EMF. For a coil rotating with angle \theta = \omega t:

\Phi_B(t) \;=\; NBA\cos(\omega t)
\varepsilon(t) \;=\; -\frac{d\Phi_B}{dt} \;=\; NBA\omega\sin(\omega t)
\varepsilon_0 \;=\; NBA\omega \;=\; (200)(0.6)(0.05)(314.16) \;=\; 1885\text{ V} \;\approx\; 1.88\text{ kV}

(Faraday's law is applied per turn; with N turns the EMFs add because the turns are in series.)

Step 3. RMS EMF. For a pure sinusoid the RMS value is the peak divided by \sqrt{2}:

\varepsilon_\text{rms} \;=\; \frac{\varepsilon_0}{\sqrt{2}} \;=\; \frac{1885}{1.414} \;\approx\; 1333\text{ V} \;\approx\; 1.33\text{ kV}

Step 4. Sanity check against the grid. Real power-station generators output tens of kV (Tehri hydroelectric plant: 11–22 kV before step-up transformers; Singrauli coal plant: 15.75 kV). Our toy number 1.33 kV is the right order of magnitude for a moderately sized rotor — the scale-up comes from more turns, bigger area, and stronger field.

Result. Peak EMF \approx 1.88 kV; RMS EMF \approx 1.33 kV, at 50 Hz.

What this shows. Every electricity generator — steam turbine at NTPC Singrauli, water turbine at Tehri, wind turbine in Tamil Nadu — reduces to a rotating coil in a magnetic field (or, equivalently, a rotating field past a fixed coil). The physics is pure Faraday. The frequency is locked to the rotation rate: 50 Hz in India (3000 rpm for a 2-pole machine), 60 Hz in the US (3600 rpm). Every Indian Railways traction transformer, every colony step-down transformer outside your flat, every laptop charger — all exist because a changing flux produces an EMF.

Common confusions

You have the working law, the experiments, the three change-mechanisms. What follows is for JEE Advanced: the integral and differential forms, Faraday's law in moving media, and the deep connection to Maxwell's equations.

Faraday's law in differential form — the Maxwell-Faraday equation

Apply Stokes' theorem to the integral form:

\oint_C \vec{E}\cdot d\vec{\ell} \;=\; \int_S (\nabla\times\vec{E})\cdot d\vec{A}

Equating this to -d\Phi_B/dt = -\int_S (\partial\vec{B}/\partial t)\cdot d\vec{A} and demanding that the equality hold for every surface, the integrands must be equal:

\boxed{\;\nabla\times\vec{E} \;=\; -\frac{\partial\vec{B}}{\partial t}\;}

This is the Maxwell-Faraday equation — one of the four field equations of electromagnetism. It says: a time-varying \vec{B} creates a rotational ("curling") \vec{E}. Combined with Ampere's law (current plus time-varying \vec{E} creates rotational \vec{B}), it supports self-propagating disturbances — electromagnetic waves. Light, radio, microwaves, X-rays, the entire EM spectrum exists because of the Maxwell-Faraday and Ampere-Maxwell equations together.

The two contributions to d\Phi/dt

For a loop whose shape and position may both be changing while \vec{B} varies with time, the total rate of change of flux decomposes cleanly:

\frac{d\Phi_B}{dt} \;=\; \int_S \frac{\partial\vec{B}}{\partial t}\cdot d\vec{A} \;+\; \oint_C (\vec{v}\times\vec{B})\cdot d\vec{\ell}

(where \vec{v} is the local velocity of the loop wire at each point, and a minus sign has been absorbed by swapping the cross-product orientation). The first term is the transformer EMF — due to the field changing in time at fixed points; the second is the motional EMF — due to the conductor moving through a static field. In most problems one or the other dominates; in general both contribute, and the total is what Faraday's law gives you in one go.

Non-conservative electric fields

For a conservative \vec{E} field (the kind produced by static charges), \oint\vec{E}\cdot d\vec{\ell} = 0 for every closed path. Faraday's law says that when \vec{B} is changing, this integral is non-zero. Therefore the induced \vec{E} cannot be derived from a scalar potential; there is no "voltage function" V such that \vec{E} = -\nabla V globally. Instead you need the vector potential \vec{A}: \vec{E} = -\nabla V - \partial\vec{A}/\partial t. The scalar potential alone works only in static situations. This is why "voltage" is not always uniquely defined in a circuit with changing flux — you can get different answers for the "voltage between two points" depending on which path you choose if flux is changing through the loop made by those two paths and the voltmeter leads.

The betatron — accelerating particles with a changing \vec{B}

A betatron is a particle accelerator that exploits Faraday's law directly: a circular region of magnetic field is ramped up in time; the induced \vec{E} field around concentric circles pushes charged particles tangentially. The famous betatron condition (2:1 rule) says: for a particle to stay on a circle of radius r while being accelerated, the average \vec{B} inside the orbit must be exactly twice the \vec{B} at the orbit. You can derive this by setting the centripetal requirement (from the \vec{B} at the orbit) equal to the rate of momentum gain (from Faraday-induced \vec{E}). Electron betatrons at TIFR in the 1950s — India's first generation of high-energy accelerators — worked exactly this way.

Faraday and relativity

If a magnet is stationary and a loop moves, the loop-frame physicist uses the Lorentz force \vec{v}\times\vec{B} to derive the EMF. If the loop is stationary and the magnet moves, the loop-frame physicist uses Faraday's law — there is an induced \vec{E} field. Einstein's 1905 relativity paper opens by pointing out that these two descriptions give the same observable EMF (measured by an ammeter in the loop), yet they use completely different "causes." Relativity resolves the tension: \vec{E} and \vec{B} are components of a single electromagnetic field tensor, and a boost mixes them. What looks like a pure \vec{B} in one frame is a mix of \vec{E} and \vec{B} in another. Faraday's law is built into the structure of spacetime.

Eddy currents — Faraday's law on bulk conductors

Faraday's law does not restrict itself to thin loops. In a solid conductor exposed to a time-varying \vec{B}, induced \vec{E} fields drive continuous current loops called eddy currents. These dissipate energy as heat (P = J^2/\sigma per unit volume). Indian Railways trains on the Mumbai–Ahmedabad and Delhi–Agra routes use eddy-current braking: a powerful electromagnet mounted near the rail creates a field that sweeps past the aluminium brake track, inducing eddy currents that dissipate kinetic energy as heat. Induction cooktops heat tawas the same way; tokamaks lose power the same way; transformer cores are laminated (thin insulated iron sheets) specifically to disrupt eddy-current paths and keep efficiency high. Every one of these is a direct consequence of Faraday's law applied to a bulk conductor.

Where this leads next