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Physics · 术语表

什么是 The quasi-stationary approximations?

Definition 11.12 University Physics — Year 2 · 第 11 章 — Maxwell’s Equations

A system of size LL driven at frequency ff is quasi-stationary when L≪λ=c/fL \ll \lambda = c/f: the time L/cL/c the fields need to cross it is negligible compared with the period, and all its points "see" the sources at the same instant. Two limits are used:

  • the magnetic quasi-stationary regime (circuits with currents, coils, transformers, induction): the displacement current is dropped from Ampère’s law, curl→⁡B→=μ0j→\operatorname{\vect{curl}}\vect B = \mu_0\vect j (so div⁡j→=0\operatorname{div}\vect j = 0 and currents flow in closed circuits), while Faraday’s law is kept in full;
  • the electric quasi-stationary regime (a charging capacitor): Faraday’s term is dropped, E→\vect E is the electrostatic field of the instantaneous charges, while the displacement current is kept to find B→\vect B.
Size against frequency: below the line L = /10 (dashed) a device is quasi-stationary and the circuit laws hold; near and above L = the fields propagate, and the device radiates.
Size against frequency: below the line L=λ/10L = \lambda/10 (dashed) a device is quasi-stationary and the circuit laws hold; near and above L=λL = \lambda the fields propagate, and the device radiates.

示例

Example 11.13 (Circuits and antennas)

A mains circuit at 50 Hz50\,\mathrm{Hz} (λ=6000 km\lambda = 6000\,\mathrm{km}) is quasi-stationary up to the size of a country — it is why Kirchhoff’s laws and the transformer work. A 10 cm10\,\mathrm{cm} circuit is quasi-stationary up to some 100 MHz100\,\mathrm{MHz}; at 1 GHz1\,\mathrm{GHz} (λ=30 cm\lambda = 30\,\mathrm{cm}) its wires are antennas, currents differ along a wire, and the circuit radiates: the domain of Chapter 17 and of microwave design, where a track on a board is a transmission line.

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