Maxwell waves, energy flow and boundary conditions
GRE Subject Test · GRE Physics Topic 15 5:52 English narration · English + 中文 subtitles burned in
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A charging capacitor changes the electric field across its gap even though no conduction current crosses the gap.
充电中的电容器即使没有传导电流穿过极板间隙，也会改变间隙中的电场。
This topic uses displacement current and the wave speed in a material, finds the directions of the wave fields and the radiated energy flow, and applies Maxwell's boundary conditions without confusing field components.
本主题使用位移电流和介质中的波速，确定波场的方向和辐射能流，并在不混淆场分量的前提下应用麦克斯韦边界条件。
Ampere-Maxwell law in vacuum is the line integral of B dot dl equals mu sub 0, times, I sub conduction plus epsilon sub 0, times d Phi sub E by d t.
真空中的安培-麦克斯韦定律为：B沿闭合回路的线积分等于μ₀乘以（传导电流I加ε₀乘以电通量Φ_E对时间的导数）。
The added displacement-current term depends on the time rate of electric flux through the chosen surface.
新增的位移电流项取决于穿过所选曲面的电通量随时间的变化率。
It ensures consistent results for a loop whose spanning surface either crosses a capacitor wire or passes between the plates.
它确保了对于跨越电容器导线或穿过极板之间的回路，无论其张成的曲面如何选取，结果都保持一致。
Displacement current is not magnetic flux or an integral over earlier electric flux.
位移电流并非磁通量，也不是对先前电通量的积分。
For a uniform plate field, the gap contribution is epsilon sub 0, times A, times d E by d t.
对于均匀极板场，间隙的贡献为ε₀A乘以电场E对时间的导数。
Signs follow the oriented surface.
符号由曲面的定向决定。
In a homogeneous, linear, lossless dielectric with permeability mu and permittivity epsilon, Maxwell's equations give a wave speed v equal to 1 over the square root of mu epsilon, and a refractive index n equal to c over v, which is the square root of mu r epsilon r.
在具有磁导率μ和介电常数ε的均匀、线性、无损耗介质中，麦克斯韦方程组给出波速v等于1除以根号下με，折射率n等于c除以v，即根号下μr乘以εr。
For nonmagnetic material mu r is about 1, so v equals c over the square root of epsilon r.
对于非磁性材料，μr约等于1，因此v等于c除以根号下εr。
Use the stated frequency-dependent material constants when dispersion matters; a static dielectric constant need not describe every optical frequency.
当色散效应显著时，请使用给定的频率相关材料常数；静态介电常数未必适用于所有光学频率。
Vacuum waves have E over B equal to c; in this simple medium the relation is E over B equals v.
真空中E除以B等于c；在此简单介质中，该关系为E除以B等于v。
For a plane wave travelling along unit vector n, B equals n cross E, over v.
对于沿单位矢量 n 传播的平面波，B 等于 n 叉乘 E 除以 v。
Both fields are perpendicular to propagation and to each other.
两个场均垂直于传播方向且彼此垂直。
A phase of k z minus omega t propagates toward positive z, while k z plus omega t propagates toward negative z.
相位 k z 减 omega t 向正 z 方向传播，而 k z 加 omega t 向负 z 方向传播。
If E is along x plus y and propagation is along positive z, B is along minus x plus y, because z cross x is y and z cross y is minus x.
若 E 沿 x 加 y 方向，且传播方向为正 z，则 B 沿负 x 加 y 方向，因为 z 叉乘 x 等于 y，且 z 叉乘 y 等于负 x。
The Poynting vector, S equals E cross H, or E cross B over mu in this medium, points along energy transport.
坡印廷矢量 S 等于 E 叉乘 H，在该介质中即为 E 叉乘 B 除以 mu，指向能量传输方向。
In the radiation zone of an accelerating charge, energy flux is outward from the source, not necessarily in the instantaneous direction of charge motion.
在加速电荷的辐射区，能流从源向外辐射，不一定沿电荷运动的瞬时方向。
Maxwell’s divergence equation ∇·B=0 gives continuity of the normal B component across an interface: a thin pillbox has no magnetic charge inside.
麦克斯韦散度方程 ∇·B = 0 表明法向 B 分量在界面处连续。 一个薄药盒内部没有磁荷。
The tangential H jump is related to surface current; it need not vanish.
切向 H 的跃变与面电流有关，它不一定为零。
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.
在理想的超导迈斯纳态模型中，若内部 B 为零，则边界处的外部法向分量必须为零，因此任何非零的外部 B 都平行于表面。
This conclusion is conditional on the stated zero-interior model; it does not follow by assuming all exterior field is zero.
这一结论依赖于所陈述的内部为零的模型；它并非通过假设所有外部场为零而得出的。
For electrostatics, normal D can instead jump by free surface charge.
对于静电学，法向 D 可因自由面电荷而发生跃变。
A plane wave travels along z in a nonmagnetic dielectric of relative permittivity 9.
一列平面波沿 z 方向在相对介电常数为 9 的非磁性电介质中传播。
Its speed is c over root 9: 3 times 10 to the 8 over 3, which is 1 times 10 to the 8 metres per second.
它的速度等于 c 除以根号 9：3 乘 10 的 8 次方除以 3，即 1 乘 10 的 8 次方米每秒。
With E along x and travel along z, B points along y.
电场沿 x 方向、波沿 z 方向传播时，B 沿 y 方向。
For an electric amplitude of 200 volts per metre, B is E over v: 200 over 1 times 10 to the 8, which is 2 microtesla.
电场振幅为每米 200 伏时，B 等于 E 除以 v：200 除以 1 乘 10 的 8 次方，即 2 微特斯拉。
E cross H then points along the direction of travel.
E 叉乘 H 指向传播方向。
A vacuum plane wave travels along negative x, with electric field along positive z.
真空中平面波沿负x方向传播，电场沿正z方向。
Determine magnetic-field direction and average energy flux for peak electric amplitude E sub zero.
求峰值电场振幅E0对应的磁场方向和平均能流密度。
A perfect absorber of area A is normal to the beam.
面积为A的完美吸收体垂直于光束放置。
Find its mean force.
求其平均作用力。
B vector equals n hat cross E vector divided by c points along positive y since negative x hat cross z hat equals y hat.
B矢量等于n帽叉乘E矢量除以c，方向沿正y轴，因为负x帽叉乘z帽等于y帽。
The expectation value of S equals E sub zero squared divided by two mu sub zero c, which equals epsilon sub zero c E sub zero squared divided by 2 for a sinusoid.
S的期望值等于E零平方除以2mu零c，即epsilon零cE零平方除以2（正弦波情形）。
Absorbed power is the expectation value of S times A and force magnitude is the expectation value of S times A divided by c, along negative x.
吸收功率为S的期望值乘以A，力的大小为S的期望值乘以A除以c，方向沿负x轴。
Award magnetic direction, mean flux, power and force or direction.
评分点包括磁场方向、平均能流、功率及力或方向。
A perfect reflector would double the force; it is a different boundary condition.
理想反射器会使力加倍；这是不同的边界条件。
Displacement current uses changing electric flux.
位移电流使用变化的电通量。
Zero interior B fixes the exterior normal component, not every exterior component.
内部磁场为零固定了外部法向分量，而非所有外部分量。
Distinguish wave propagation from particle motion.
区分波的传播与粒子的运动。
displacement current: Electric-flux time-derivative contribution in Ampere–Maxwell law.
位移电流。 安培-麦克斯韦定律中的电通量时间导数贡献。
Poynting vector: Electromagnetic energy flux per unit area and time.
坡印廷矢量。 单位面积和时间的电磁能量通量。
Retrieve the meanings without reading the definitions, then change a parameter in the original transfer and test the limiting case.
不阅读定义，直接回忆其含义；然后改变原始传递中的一个参数，并检验极限情况。