E电磁波

ε0
ε0
∫∫
( S0 + S 2 )
dt ∫∫( S0 + S 2 )
dt
Maxwell reasoned that either real current, I, or displacement current , Id, (or both) might flow any given surface, but the sum I+Id that flows into any region must also flow out. Total current： ：
v v ∫∫ D ⋅ dS =0L (1) v v dΦ m E ⋅ dl = − L (2) ∫l dt
v v ∫∫ B ⋅ dS = 0LL (3)
∫
l
v v H ⋅ dl =
∫∫
S
v v ∂D ⋅ dS L (4) ∂t
(2) Differential shape
（4）the boundary condition ） 电磁场边值条件
The difference between electrostatic field and induced electric field： ：
一个有源、一个无源; 异： 同： 对电荷有力的作用。
v v Electrostatic field: ∫ E(1) ⋅ dl = 0 v v w v v v v ∂B v dΦm E ⋅ dl = ∫ E(1) ⋅ dl + ∫ E( 2 ) ⋅ dl = − ∫∫ ⋅ dS = − ∫
The integrans
v v ∫∫ D ⋅ dS = ∑ qi LLLLLLLLL (1)
Meaning: Gauss’s law for electricity. Comes directly from Coulomb’s law. The electric flux out of a region is proportional to the net charge inside. v v v v v v v ∂B dΦ m E = E(1) 静 + E( 2 )涡 = − ∫∫ ⋅ dS L (2) ∫l E ⋅ d l = −
L
S1
S2
C
S2
v v j ⋅ dS = i 稳恒情况下得到 的安培定理不能 v v j ⋅ dS = 0 用于交变电路中
On the other hand, because no current is emerging, charge is building up inside, and as a result, electric flux is building up between the capacitor plates, and therefore, flux lines pass through the hemispherical surface. The electric flux is given by Φ = q / ε
v v v D = D(1) + D( 2 ) v v v B = B(1) + B( 2 )
v v ∫∫ D1 ⋅ dS = ∑ qi v v ∫∫ B(1) ⋅ dS = 0
v v ∫∫ D2 ⋅ dS = 0 v v ∫∫ B( 2) ⋅ dS = 0
v v v D = D(1)静 + D( 2 )涡
v v Surface S1： ∫ H ⋅ dl = ∫∫ S1 v v Surface S 2： ∫ H ⋅ dl = ∫∫
Ampere’s circuital theorem fails in the circuit shown in right Fig: 在研究含有电容( 在研究含有电容(capacitor)的 ) 交变电流电路时， 交变电流电路时，应用安培环 路定理就会出现矛盾。 路定理就会出现矛盾。
The total field at a point in space:
v v v E = E (1) + E ( 2 )
v E (1) : 静电场 , 有源场 ;
Electrostatic field
v Curl electric field or E( 2) : 涡旋电场 , 无源场. induced electric field
Chapter16 Electromagnetic field Electromagnetic Wave
§1 Maxwell’s electromagnetic theory
§2 Maxwell’s equations §3 Electromagnetic wave §4 Examples
§1 Maxwell’s electromagnetic theory
The same: 二者都可产生磁场 二者都可产生磁场 The difference： ： 1 位移电流的实质是变化的电场而非电荷的定向移动 位移电流不仅在导体中而且在介质和真空中存在。 2 位移电流不仅在导体中而且在介质和真空中存在。 位移电流不产生焦耳热。 3 位移电流不产生焦耳热。
§2 Maxwell’s equations
dq dΦ d Id = = dt dt
在电容器中无传导电流但有 变化的电场，有电位移。 变化的电场，有电位移。
L
S0
S1
S2
C
Maxwell thought of the term dΦ d / dt as representing a kind of fictitious current to complete the circuit that is interrupted by the capacitor. It is called Displacement current dq dΦ d Id = = dt dt v v dq v v d σ D E= = D ⋅ dS = q = σS D ⋅ dS =
1 Maxwell’s first supposition-curl electric field
dΦ → ε i → Ii Faraday: dt v dΦ → E涡 → ε i → Ii Maxwell： ： dt v v v dΦm ∂B v ε i = ∫ Ei ⋅ dl = − = − ∫∫ ⋅ dS L dt ∂t
dt ∂t
Meaning: Faraday’s law of electromagnetic induction. A changing magnetic flux creates an electromotive force.
v v ∫∫ B ⋅ dS = 0LLLLLLLLLL (3)
v v v B = B(1) 传 + B( 2 ) 位
e 0
（2） The correction of Ampere’s circuital theorem ） The supposition of displacement current 矛盾是由电流变化造成的， 矛盾是由电流变化造成的，即传导电流在交变电容 电路中不再连续； 电路中不再连续；如果假设在变化的电容器中有另一种 电流存在，整个电路的电流就又连续了。 电流存在，整个电路的电流就又连续了。 Maxwell argued that this buildup of electric flux could be just what’s needed to correct Ampere’s equation. The flux is related to the current flowing into the region by equation:
∂t dt
v v dΦm ∫ E ⋅ d l = − dt
实质: 实质 A circulating electric （1） field can be created by a ） changing magnetic field.
Faraday’s law of electromagnetic induction. A changing magnetic flux creates an electromotive force.
Meaning: Gauss’s law for magnetism. Because there ere no magnetic monopoles, there is never any net flux out of any region.
∫
l
v v H ⋅ dl =
∑
I传 +
∫∫
S
v v ∂D ⋅ dS L (4) ∂t
I = ∑ I0 + ∑ Id
To generalize Ampere’s circuital theorem by replacing I by I+Id
v v ∫ H ⋅ dl = ∑ I
v v ∫ H ⋅ dl =
v v ∫∫SD ⋅ dS v v v ∂D v ∫ H ⋅ dl = ∑ I 0 + ∫∫S ∂t ⋅ dS L L ( 2 ) Note : Displacement and conducting currents d ∑ I 0 + dt
2 Maxwell’s second supposition ---displacement current 位移电流
麦克斯韦对电磁场理论的重大贡献的核心是位移电 流的假说， 流的假说，它是将安培环路定理应用于含有电容的交变 电路中出现矛盾而引出的。 电路中出现矛盾而引出的。 C （1） Ampere’s circuital theorem ） v v Constant current： ∫ H ⋅ dl = ∑ I i ： Ampere’s law states that the same equation holds if the plane circular region is replaced by any surface having C as its boundary. 通过以环路为周界所有曲面的电流相等， 通过以环路为周界所有曲面的电流相等，与曲面形 位置无关。 状、位置无关。
v ∇ ⋅ D = ρ e0 v v ∂B ∇× E = − ∂t v ∇⋅B = 0 v v v ∂D ∇ × H = j0 + ∂t
(3) Matter equation
v v D = ε rε 0 E v v B = µ r µ0 H v v j0 = σ E
当界面两边为介质时： 当界面两边为介质时： v σ e0 = 0 j0 = 0 v v v v v v n ⋅ ( D2 − D1 ) = 0 n × ( E2 − E1 ) = 0
v v v n ⋅ ( D2 − D1 ) = σ e 0 σ e 0 : Free charge v facial density v v n × ( E2 − E1 ) = 0 v v v v j0 : Conducting n ⋅ ( B2 − B1 ) = 0 current facial v v v v n × ( H 2 − H 1 ) = j0 density
v v v H = H (1) 传 + H ( 2 ) 位
Meaning: Maxwell-Ampere law. Circuital magnetic fields are created either by electric currents or by changing electric flux. Appendix: (1) Maxwell’s equations in free space:
v v v n ⋅ ( B2 − B1 ) = 0 v v v n × ( H 2 − H1 ) = 0
1 Electromagnetic wave
§3 Electromagnetic wave
A changing magnetic field can produce an electric field. A changing electric field can produce a magnetic field. Waves arise when these two are combined. The dynamic E and B can be created by each other. This is the essence of the electromagnetic wave. 变化的电场和变化的磁场相互激发，在空间传播开来， 变化的电场和变化的磁场相互激发，在空间传播开来， 形成电磁波。 形成电磁波。