浙江大学大学物理甲下 chapter 38

1、Chapter 38 Maxwells Equations and Electromagnetic Waves138-1 The Basic Equations of Electromagnetism Consider the similarities of electric and magnetic fields in their mathematical properties. Gausslaws for electricity and magnetism are symmetrical for a region of space in which electric and magneti

2、c fields exist but there are no charges or currents.Faradays law and Amperes law are not symmetrical for a closed path in this region.2 Is it possible that a varying electric field could set up a magnetic field? Yes it is!38-2 Induced Magnetic Field and the Displacement CurrentDoes Amperes law becom

3、e invalid?3generalization of Amperes law A changing electric field can produce a magnetic field.4A beautiful example of the symmetry of nature.5If we define as id, Displacement current6Displacement Current* The displacement current in the gap equals the conduction current in the wires.The density of

4、 displacement current7Quick Quiz-1 In an RC circuit, the capacitor begins to discharged. During the discharge, in the region of the space between the plates of the capacitor, there is (1) conduction current but no displacement current. (2) displacement current but no conduction current. (3) both con

5、duction and displacement current. (4) no current of any type.8Quick Quiz-2 The capacitor in an RC circuit begins to discharge. During the discharge, in the region of the space between the plates of the capacitor, there is (1) an electric field but no magnetic field. (2) a magnetic field but no elect

6、ric field. (3) both electric and magnetic fields. (4) no fields of any type. 938-3 Maxwells EquationsName Equation Describes Crucial ExperimentGause law for electricityCharge and the electric fieldGause law for magnetismMagnetic fieldFaradays law of inductionAmperes lawThe electrical effect of a cha

7、nging magnetic fieldThe magnetic effect of a current or a changing electric field10 When the equations are combined, a new prediction does emergethe existence of electromagnetic waves and a value for their speed.1138-4 Generating an Electromagnetic Wave If an electric charge is at rest or the charge

8、 is moving at constant speedThere is no transport of energy or momentum.There is no electromagnetic radiation.If the charge is accelerated: electromagnetic radiation12dipole antennaoscillating electric dipoleelectric dipole radiation13Radiation from oscillating dipole*141538-5 Traveling Waves and Ma

9、xwells Equations1. Differential forms of Maxwell equations For the space apart from the source there are not the distribution of charges and currents,1617Suppose the wavefronts are the planes, E=E(x,t), B=B(x,t), this means the E and B are independent on y, and z. Thus we have:1819For Ex, For Bx,Ex

10、and Bx is static field. Suppose they are zero. This means the electric field E and magnetic field B are all perpendicular to the x axis. 20 Then we choose a new coordinate system. Let E=Ey j, Ez=0, thus By is static field. Suppose it is zero. We obtain B=Bzk. This means the electric field E is perpe

11、ndicular to the magnetic field B.21For Ey and Bz, These are wave equations. Their simplest solutions are: 22Conclude: (1) EB, and Ei, Bi, i is the direction of the wave propagating. EB= 0Si.(2) E and B are in phase.(3) Polarization of electromagnetic waves.(4) The speed of electromagnetic wave is “c

12、”, the speed of light.2324Substitute the solutions, Substitute the solutions, 2538-6 Energy Transport and the Poynting Vector The direction of the propagation of the electromagnetic wave is given by: This wave carries energy. The energy flow per second and per unit area is:1m2cwave26Define the Poynt

13、ing vector S as:The direction of S is the direction of propagation of the wave. The magnitude of S is directly related to the energy being transported by the wave:27The Intensity of a wave is the time-average of S:The energy density of the electromagnetic wave is: 28 The magnitude of the Poynting ve

14、ctor gives the rate of energy flow. It is the energy of the wave flowing through per unit area in per unit time.29Quick Quiz-3 An electromagnetic wave propagates in the y direction. The electric field at a point in space is momentarily oriented in the +x direction. The magnetic field at that point i

15、s momentarily oriented in the (1) x direction (2) +y direction (3) +z direction (4) z direction.30Quick Quiz-4 Which of the following is constant for a plane electromagnetic wave? (1) magnitude of the Poynting vector (2) energy density uE (3) energy density uB (4) wave intensity.31 Wave with plane w

16、avefront, e.g. light from a laser or light from the Sun, its amplitudes Em and Bm is constants, the intensity does not change with location as the wave travels. Wave with sphere wavefront, e.g. a point source of wave in isotropically, the energy in any spherical wavefront remains constant. But the p

17、ower per unit area decreases when the radius r increases.*32Example: A parallel plate capacitor with circular plates is been charging. Find the energy entering into the capacitor.Solution:The direction of S is towards to the axes with perpendicular to it.333438-7 Radiation PressureEnergy transport momentumMomentum = Intensity = Radiation Pressure35Apparatus for measuring radiation pressure36Light pressure, though “light”, has noticeable effects comets tail pushed away from the sun.The momentum density of electromagnetic wave37Intensive rea