第17章 电磁感应和电磁波.pptx

1、CHAPTER 17 ELECTROMAGNETIC INDUCTION AND ELECTROMAGNETIC WAVE,17.1 Faradays Law of Electromagnetic Induction 17.2 Motional Emf 17.3 Induced Emf and Induced Electric Field 17.4 Mutual Induction 17.5 Self-induction 17.6 Energy Stored in Magnetic Field 17.7 Maxwells Equations 17.8 Electromagnetic Waves

2、 (EM Waves) 17.9 Energy in EM Waves,17.1 Faradays Law of Electromagnetic Induction,When the magnetic flux through the area surrounded by a closed conducting loop is changing with time ,electric current is produced in the loop. This current is called the induction current. The emf which produces indu

3、ction current in a conducting loop when the magnetic flux through the loop is changing is called the induction emf (electromotive force),Experiments shows that the magnitude of the induction emf produced in a conducting loop is proportional to the time rate of the change of the magnetic flux through

4、 the loop, the direction of the emf depends on the direction of the magnetic field and the condition of the changing of the magnetic flux.,The general expression of Faradays law of induction.,Letbe the magnetic flux through a conducting loop and the induction emf produced in it when the magnetic flu

5、x is changing , the experimental law reads mathematically,When the direction of the magnetic field is related to the positive direction along the loop by righthand thread rule, the flux is taken to be positive. Then when the flux through the loop is increasing, d d 0,Eq.(17.1)gives 0, which means th

6、at the direction of the induction emf is the same as the positive direction of the loop.(Fig.(b),It is an example of obtaining an induction emf,The induction emf is always produced in such a direction of that the change of the induction current it brings to the loop produces a magnetic field in the

7、loop to resist the change of the magnetic flux through the loop. The regulation is called the Lenz law.,When the magnetic flux through every turn is the same , we have the total flux= then,17.2 Motional Emf,The bar is moving with constant velocity v rightwards perpendicular to its length and kept el

8、ectrically contact with the other two sides of the loop. At some instant the magnetic flux through the loop is,As the bar is moving rightwards , the area surrounded by the loop expends and then the magnetic flux through the area changes.,The Lorentz force plays the role of the non-electrostatic forc

9、e here to produce the motional emf in bar ab,As the loop is a closed one , the motional emf would produce electric current-induction current in the loop. When the current is I , the power of the motional emf is,When the bar ab moves with current in it , a magnetic force is exerting on it opposite to

10、 the direction of motion and work must be done by external agency on the bar. The magnetic force is = ,leftwards. To move the bar rightwards uniformly , an rightward external force must be applied on the bar to balance the magnetic force. Thus = ,Fig.17.6 No work done by the Lorentz force,The Lorent

11、z force on the free electron moving together with the conducting bar at velocity is given by = . Exerted by this force , the electron would move with velocity v along the rood . Due to this v, the electron would be exerted by another Lorentz force = perpendicular to the length of the bar . The net L

12、orentz force on the electron is = + ,while the resultant velocity of the electron is = + . The work done by the net Lorentz force per unit time is,Or,To keep the free electron to move at together with the bar , there must be an external force exerted on the electron to balance the force . Thus = ,Th

13、e Lorentz force does no work here expresses actually energy conversion and energy conservation. Here the Lorentz force plays the role of an energy transmitter,17.3 Induced Emf and Induced Electric Field,For a stationary conducting loop , when the magnetic field confined by it changes with time , the

14、 magnetic flux through it changes also, and then at the same time an induction emf is produced in the loop. The induction emf so produced is called the induced emf.,The induction current is formed by the charge originally at rest macroscopically under the action of non-electrostatic force and the fo

15、rce on a charge at rest can only be electric force, then the non-electric force should be an electric force. Since this electric field is produces be changing magnetic field , it is called the induced electric field,The induced emf produced in a closed conducting loop L due to the change of the magn

16、etic field in it is,Faradays law :,Maxwell advanced that when the magnetic field changes with time , not only an induction emf is produced in a material conducting loop. But also an electric field, is produces everywhere in the space around . The circulation of the induced electric field along any c

17、losed path is given by the Eq. (17.11),In general, there are in space both electrostatic fields , and induced electric field . According to the principle of superposition, the net electric field = + , and the line integral of along any closed path L is equal to the sum of the circulation of and alon

18、g the same closed path. Since the circulation of is always zero ,we have,17.4 Mutual Induction,When the current in a coil changes , the magnetic field around it also changes . Then in another coil nearby an induced emf will be induced. Such induced emf is called mutual induction emf,There are two co

19、ils L1 and L2 . The mutual induction emf in coil L2 is brought about by the changing with time of current i1 in coil L1 and denoted by 21 .the relation between 21 and i1 is given as follows.,The proportionality constant 21 is called the coefficient of mutual induction of coil L1 to coil L2,Faradays

20、law :,With the same argument , the total magnetic flux through L1 due to i2 is proportional to i2,And,It can be proved that for a given pair of coils,M is called the coefficient of mutual induction of the two coils or simply their mutual inductance,In SI , the unit of mutual inductance is henry, abb

21、reviated as H.,17.5 Self-induction,When the current I in a coil changes with time , the total magnetic flux through the coil itself also changes and then an induced emf will be produced in the coil itself. This phenomenon is called the self-induction and the induced emf produced in the coil is calle

22、d self-induction emf. The coil itself is called an inductor .,The proportionality constant L is called the coefficient of self-induction of self-inductance of simply inductance which is determined by the dimension ,shape, number of turns of the inductor and the material around it .dimension,The self

23、-induction emf is always produced in the direction such that it resists the change of the current . This is consistent with Lenz law determing the direction of the induction emf.,Fig.17.13 Self-induction phenomena (a) The key is closed; (b) the key is opened,17.6 Energy Stored in Magnetic Field,In t

24、he experiment ,after the key is opened, the source no longer supplies energy to the bulb, where the energy dissipated in the strong flash comes from? Since the current producing the flash is the current brought about by the self-induction emf in the coil and this current diminishes and dies out toge

25、ther with the magnetic field in the coil, we may consider the energy producing the flash is originally stored in the inductor or ,more definitely , in the magnetic field in the inductor. This energy is thus called the magnetic energy.,The magnetic energy:,It is considered as stored in the magnetic f

26、ield produced by the current I flowing in an inductor of inductance L,For the energy stored in magnetic field, the idea of energy density can also be introduced.= 2 and he energy stored in the solenoid is,Since the magnetic field in the solenoid is=,Since the magnetic field is concentrated in the so

27、lenoid with volume V, the energy density of the magnetic field is,Or,17.7 Maxwells Equations,The behavior of electric and magnetic waves can be fully described by a set of four equations (which we have learned already).,Gausss Law for magnetism,Gausss Law for electricity,Amperes Law,Faradays Law of

28、induction,Gausss Law for magnetism,Gausss Law for electricity,Amperes Law,Faradays Law of induction,To find the action on a charged particle by electric and magnetic fields and then to predict the motion of the particle , the following formula Lorentz force is also needed,17.8 Electromagnetic Waves

29、(EM Waves),When a charge is accelerated , the electric can magnetic fields around it will change with time and the change will propagate outward from the location of the charge. This closely related changing electric and magnetic fields are called electromagnetic wave.,(a) It is transverse wave, its electric field and magnetic field are both perpendicular to he velocity of propagation,(b) Its and are also perpendicular to each other . , and in order form a righthand t