GRE · GRE Subject Test · GRE 物理 · 知识点 15
A charged capacitor can change its electric field across a gap even though no conduction current crosses the gap.
Prerequisites: 13, 29, 47.
| English | 中文 | 拼音 |
|---|---|---|
| displacement current/dɪˈspleɪsmənt ˈkʌrənt/ | 位移电流 | wèi yí diàn liú |
Ampere–Maxwell law in vacuum is ∮B·dl=μ0(I_conduction+ε0 dΦE/dt). The added displacement-current term depends on the time rate of electric flux through the chosen surface. It ensures consistent results for a loop whose spanning surface either crosses a capacitor wire or passes between the plates. Displacement current is not magnetic flux or an integral over earlier electric flux. For a uniform plate field, the gap contribution is ε0A dE/dt; signs follow the oriented surface.
In a homogeneous, linear, lossless dielectric 电介质 with permeability μ and permittivity ε, Maxwell equations give wave speed v=1/sqrt(με) and refractive index n=c/v=sqrt(μrεr). For nonmagnetic material μr≈1, so v=c/sqrt(εr). Use the stated frequency-dependent material constants when dispersion matters; a static dielectric constant need not describe every optical frequency. Vacuum waves have E/B=c; in this simple medium the relation is E/B=v.
| English | 中文 | 拼音 |
|---|---|---|
| dielectric/ˌdaɪɪˈlektrɪk/ | 电介质 | diàn jiè zhì |
For a plane wave travelling along unit vector n, B=(n×E)/v. Both fields are perpendicular to propagation and to each other. Phase kz−ωt propagates toward +z, while kz+ωt propagates toward −z. If E is along x+y and propagation is +z, B is along −x+y, because z×x=y and z×y=−x. The Poynting vector 坡印廷矢量 S=E×H (E×B/μ in this medium) points along energy transport. In the radiation zone of an accelerating charge, energy flux is outward from the source, not necessarily in the instantaneous direction of charge motion.
| English | 中文 | 拼音 |
|---|---|---|
| Poynting vector/ˈpɔɪntɪŋ ˈvektə/ | 坡印廷矢量 | pō yìn tíng shǐ liàng |
Maxwell’s divergence equation ∇·B=0 gives continuity of the normal B component across an interface: a thin pillbox has no magnetic charge inside. The tangential H jump is related to surface current; it need not vanish. Under an ideal superconducting Meissner-state model with zero interior B, the exterior normal component at the boundary must therefore be zero, leaving any nonzero exterior B tangent to the surface. This conclusion is conditional on the stated zero-interior model; it does not follow by assuming all exterior field is zero. For electrostatics, normal D can instead jump by free surface charge.
A plane wave travels along positive z in a linear lossless nonmagnetic dielectric. With relative permittivity 9,
Displacement current uses changing electric flux. Zero interior B fixes the exterior normal component, not every exterior component. Distinguish wave propagation from particle motion.
displacement current: Electric-flux time-derivative contribution in Ampere–Maxwell law.
Poynting vector: Electromagnetic energy flux per unit area and time.
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