Induction heating: cross-section (2D)

An alternating current in a coil makes an alternating magnetic field. By Faraday's law the changing flux drives circular eddy currents in a nearby conducting plate, E_theta(r) ~ (r/2) dB/dt, and the plate warms by Ohmic loss sigma E^2 (induction heating). The field penetrates only about one skin depth delta = 1/sqrt(pi f mu0 sigma), so the effective heated thickness is delta(1 - e^(-t/delta)).

What this 2D view adds

• A cross-section through the axis: flux lines from a real Biot-Savart tracing, eddy-current directions in the plate and a temperature-coloured plate.
• Radial profile of field and loss density, the temperature curve against its equilibrium, and a frequency sweep.

Honest simplifications

Quasi-static, non-ferromagnetic circular plate, a Gaussian radial field shape and no back-reaction of the plate on the coil. This is an educational estimate, not a finite-element model. Same physics module as the 3D page.