Why an electric field — not magnetic — heats water, and why magnetization $M$ — not skin depth — heats your pan. A walk through the gap between common intuitions and the actual physics.
A microwave oven uses microwaves, which are electromagnetic waves — they carry both an electric field $\mathbf{E}$ and a magnetic field $\mathbf{B}$. But heating water is done almost entirely by the electric field.
Water molecules carry a permanent electric dipole moment. The oscillating $\mathbf{E}$ keeps rotating them, while the viscosity of the H-bond network in liquid water resists that rotation. The polarization lags the field in phase — this is dielectric relaxation — and that phase lag is exactly what gets dissipated as heat.
Why doesn't the magnetic field contribute? Two reasons:
(1) In an EM wave, $|\mathbf{E}|/|\mathbf{B}| = c$. The magnetic force $q\mathbf{v}\times\mathbf{B}$ on a non-relativistic particle is smaller than the electric force $q\mathbf{E}$ by a factor of $v/c$. For water molecules at thermal speeds ($\sim 600$ m/s), $v/c \sim 10^{-6}$.
(2) Water is diamagnetic. Its magnetic dipole coupling is intrinsically weak — there's almost nothing for the magnetic field to grab onto.
So the answer to "why no magnetic field?" is: there is one, but it's along for the ride. The $\mathbf{E}$ field does the work. For NMR-style heating you'd need a static $B_0$ to set up Larmor precession — which doesn't exist in a microwave oven, so no magnetic resonance.
The single most common misconception about microwave ovens: "2.45 GHz is the resonant frequency of water." It's wrong.
"2.45 GHz matches a rotational transition of water" — you see this in textbooks, popular media, and casual explanations. But 2.45 GHz is nowhere near water's absorption peak.
Liquid water's dielectric loss $\varepsilon''(\omega)$ is a broad Debye relaxation spectrum, with its peak around 17–20 GHz at room temperature (corresponding to the relaxation time $\tau \approx 8$ ps, so $1/(2\pi\tau)$). 2.45 GHz sits well below the peak, on the low-frequency tail.
So why 2.45 GHz?
2.45 GHz is reserved for industrial, scientific, and medical use — no telecom license required. A practical engineering choice.
Heating at the absorption peak would cook only the surface. 2.45 GHz is deliberately chosen away from the peak to ensure ~1 cm penetration into food.
The truth is the opposite of the popular story: 2.45 GHz is deliberately off-resonance to secure penetration. Slightly inefficient absorption is the feature, not a bug.
Photon energy vs. heating: $\hbar\omega \approx 10\ \mu$eV is roughly $1/2500$ of $k_B T(300\text{ K}) \approx 25$ meV. A picture of "one photon exciting one molecule" simply doesn't apply. Heating here is macroscopic dielectric loss; even with $\hbar\omega \ll k_B T$, as long as $\varepsilon''(\omega) \neq 0$ the medium absorbs power $\frac{1}{2}\omega\varepsilon_0\varepsilon''|E|^2$.
If microwave ovens use $\mathbf{E}$, induction cooktops use $\mathbf{B}$. A coil carries an AC current at ~25 kHz, generating an oscillating magnetic field. That field induces eddy currents in the pan, which dissipate as $J^2/\sigma$ Joule heat. Simple in principle.
Let's start with the result:
Three forms of the same expression. The cast of characters:
All three forms are the same quantity, but each one makes different variables visible and hides others. This is where most of the confusion starts.
"Skin depth is small in a ferromagnet, so the current is concentrated and it heats well." This intuition is half right — and half a trap.
"Small $\delta$ ⇒ good heating" does not hold in general. Aluminum has $\delta \approx 500\ \mu$m, tiny compared to the free-space wavelength (km scale), yet induction doesn't work on it. A superconductor has $\delta \to 0$ but absorbs zero power.
Why $\delta$ alone misleads: the surface current density is $J_0 = |\mathbf{H}|/\delta$, so smaller $\delta$ means larger $J_0$. But the heating is $\int J^2/\sigma\,dV$, and the integration volume also shrinks with $\delta$. The two effects multiply:
The relevant combination is the product $\sigma\delta$. Its inverse $1/(\sigma\delta) = \text{Re}(Z_s)$ is nothing other than the sheet resistance. Heating scales with sheet resistance.
| Material | $\delta$ (μm) | $\sigma$ (S/m) | $\sigma\delta$ | $R_\square = 1/(\sigma\delta)$ (Ω) |
|---|---|---|---|---|
| Aluminum | ~500 | 3.5×10⁷ | 1.75×10⁴ | 5.7×10⁻⁵ |
| Iron ($\mu_r \approx 500$) | ~40 | 1×10⁷ | 400 | 2.5×10⁻³ |
Aluminum's $\delta$ is 12× larger, but the real story is in $\sigma\delta$ — which is 44× larger for aluminum. So iron's sheet resistance is 44× higher, and the absorbed power scales accordingly. Looking at $\delta$ alone underestimates the gap.
Magnetization $\mathbf{M}$ contributes to heating through exactly two channels. Both originate from the same $\mu_r$, but they act in physically distinct ways.
Reading the heating formula as $P/A = \tfrac{1}{2}|\mathbf{H}_{\text{surf}}|^2 \cdot \text{Re}(Z_s)$, the left factor is Channel 1 and the right factor is Channel 2. Both effects multiply, and that's why ferromagnetic heating dominates so completely.
The letter $M$ doesn't appear explicitly, but it's hiding in both places:
On top of the eddy current loss, a ferromagnet has an additional irreversible loss per cycle: $\oint \mathbf{H}\cdot d\mathbf{B}$ (the area of the B-H loop).
This mechanism is unrelated to eddy currents — it's about the irreversibility of domain wall motion. Even an idealized $\sigma \to \infty$ ferromagnet would still have hysteresis loss. In practice it contributes 10–30% of total induction heating.
"What if a non-magnetic material has small enough $\delta$ — couldn't that work?" It's a natural question, but the answer is no — at least at the standard 25–50 kHz of household induction.
Using the two-channel framework, the reason is sharp:
"All-metal" induction cooktops: push the frequency above a few MHz, and both $\delta \propto 1/\sqrt{\omega\sigma}$ and $|Z_s| \propto \sqrt{\omega/\sigma}$ improve enough to heat non-magnetic conductors. Such products exist, but coil losses grow with frequency and the absence of flux concentration weakens coupling intrinsically. Efficiency lags far behind ferromagnetic pans.
That rule applies only to plane-wave absorption in free space. At 25 kHz, the wavelength is ~12 km and $\lambda/2\pi \sim$2 km. Induction operates in the quasi-static near-field regime, with coil and pan separated by centimeters. In near-field there is no plane-wave $|\mathbf{E}|/|\mathbf{H}|$ ratio, and absorption is governed by $|\mathbf{H}_{\text{surf}}|^2 \cdot \text{Re}(Z_s)$ — $\eta_0$ does not appear anywhere. The intuition from free-space matching doesn't transfer.
Misconception 1. "A microwave oven uses water's resonant frequency."
Reality: 2.45 GHz is an ISM band chosen for penetration depth — deliberately off-resonance. Liquid water's absorption peak is around 17–20 GHz.
Misconception 2. "Small skin depth is itself the cause of heating."
Reality: Heating scales with $1/(\sigma\delta)$. Small $\delta$ alone isn't enough — aluminum is the counterexample. $\delta$ is a byproduct of the same cause ($\mu_r \uparrow$), not the cause itself.
Misconception 3. "$M$ adds to $H$."
Reality: $\mathbf{B} = \mu_0(\mathbf{H} + \mathbf{M})$ — but $\mathbf{M}$ is not added to $\mathbf{H}$ itself. The source of $\mathbf{H}$ is the free current $\mathbf{J}_{\text{free}}$. $M$ acts indirectly by reshaping the magnetic circuit, which raises the value of $|\mathbf{H}_{\text{surf}}|$.
Misconception 4. "Impedance matching $|Z_s| = \eta_0$ is optimal."
Reality: This is a plane-wave rule. In the near-field of induction, $\eta_0$ doesn't enter the formula at all. Larger $|Z_s|$ is better (within the good-conductor regime).
Misconception 5. "Eddy currents raise the surface $H$ in a ferromagnet."
Reality: The opposite. By Lenz's law, eddy currents oppose the external change — they reduce $H$ inside the medium. The large surface $|H|$ comes from the static magnetic circuit effect (flux concentration).
A microwave oven heats water by rotating its electric dipoles against viscous drag (Debye loss). An induction cooktop heats a ferromagnetic pan by shaking its magnetization $M$ (flux concentration × eddy current amplification × hysteresis bonus). Skin depth is the length scale that emerges from these mechanisms — never their cause.