Download presentation

Presentation is loading. Please wait.

Published byAndrew Moxon Modified over 3 years ago

1
Chapter 13 Maxwell’s Equations 麦克斯韦方程组

2
Maxwell summarized the experimental laws of electricity and magnetism—the laws of Coulomb, Gauss, Biot-Savart, Ampere, and Faraday. He found that all the experimental laws hold in general except for Ampere’s law. Dones not apply to discontinuous current Invent displacement current to generalize Ampere’s law

3
§ 13-2 Maxwell’s Equations 麦克斯韦方程组 § 13-1 Displacement Current 位移电流

4
Electric field Electrostatic field --set up by static charges Induced electric field --set up by varying M-field Is there another M-field Magnetic field magnetic field --set up by steady current that it is set up by varying E-field ? ? 1.Question §13-1 Displacement Current

5
Displacement Current 位移电流 2. Maxwell’s hypothesis A varying electric field will set up a magnetic field in exactly the same way as ordinary conduction current. Varying Inducing

6
Two different surfaces S 1, S 2 bounded by the same circle L 3. 3. Displacement current The capacitor is electrified For S 1 For S 2 Ampere’s law cannot be used in this problem. Conductive current

7
Though there is any current going through the surface S 2, there is a changing -flux going through it. When I c 0,

8
Assume S--the area of plate, --the area charge density on S at time t. on S at time t. then

9
--the density of displacement current -- -- Displacement current Definition

10
--Generalized form of Ampere’s law I =Ic+IdI =Ic+IdI =Ic+IdI =Ic+Id generalized current( 全电流 ) Let -flux

11
Notes The differences between I d and I c : I c is formed by the motion of charges in conductor along one direction. I c produces Joule thermal energy in conductor. I d I c I d set up a M-field in exactly the same way as I c. I d is formed by the varying of electric field. I d is formed by the varying of electric field. I d never has thermal effect. I d can be found in the area that exists varying electric field( vacuum, dielectric, conductor).

12
[Example]Two circle plates with radius R=0.1m consist of a parallel plate capacitor. When the E-field between the plates increases with dE/dt=10 12 Vm -1 s -1. [Example]Two circle plates with radius R=0.1m consist of a parallel plate capacitor. When the capacitor is electrified, the E-field between the plates increases with dE/dt=10 12 Vm -1 s -1. Find The displacement current I d between two plates. The magnitude and direction of the M-field in the area of r R

13
Solution The distribution of E-field has axial symmetry. The distribution of E-field has axial symmetry. So the induced M-field produced by the varying E-field has the same form as a cylindrical current. Drawing a circle L with r as shown in Fig. Using generalized form of Ampere’s law, we have

14
When r<R, (r<R) i.e.

15
When r>R, (r>R) i.e.

16
When, ’s direction: L When, L

17
§13-2 Maxwell’s Equations E-Field M-Field E-Field Electromagnetic wave Maxwell’s Equations Charge Current Charge Current

18
Electrostatic field set up by static charges ： Steady magnetic field set up by steady current ： 1. Maxwell’s equations

19
Induced electric field set up by varying M-field: Induced M-field set up by varying E-field (displacement current):

20
In general, We get Maxwell’s Equations in integral form.

21
As Maxwell’s Equations in differential form. And

22
2. Electromagnetic wave Special example ： In the free space( 自由空间 ) No any charge and conductive current. Maxwell’s Equations ：

23
For vacuum, Making a Rotation( 旋度 ) for , Use Use Use

24
Using vector formula, =0 We can get the equation from above, --differential form of E-field Similarly, --differential form of M-field The wave equations of electromagnetic field in vacuum.

25
The speed of E-M-wave is E-M-field spreads in the space to form the E-M-wave. x y z o c Direction of propagation

Similar presentations

Presentation is loading. Please wait....

OK

TIME VARYING MAGNETIC FIELDS AND MAXWELL’S EQUATIONS

TIME VARYING MAGNETIC FIELDS AND MAXWELL’S EQUATIONS

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google