《电磁场与电磁波第12讲焦耳定律边界条件电阻计算及复习课件.ppt》由会员分享，可在线阅读，更多相关《电磁场与电磁波第12讲焦耳定律边界条件电阻计算及复习课件.ppt（33页珍藏版）》请在三一文库上搜索。
1、电磁场与电磁波第12讲焦耳定律边界条件电阻计算及复习,1,Field and Wave Electromagnetic 电磁场与电磁波,2015. 10.31,电磁场与电磁波第12讲焦耳定律边界条件电阻计算及复习,2,1. Current Density and Ohms Law,Review,电磁场与电磁波第12讲焦耳定律边界条件电阻计算及复习,3,3. Equation of Continuity and Kirchhoffs Current Law,2. Electromotive Force and Kirchhoffs Voltage Law,电磁场与电磁波第12讲焦耳定律边界条件电
2、阻计算及复习,4,We are now in a position to prove this statement and to calculate the time it takes to reach an equilibrium.,where 0 is the initial charge density at t = 0.,The time constant t is called the relaxation time(驰豫时间）. 铜，=1.5210-19S,An initial charge density 0 will decay to 1/e or 36.8% of its v
3、alue in a time equal to,电磁场与电磁波第12讲焦耳定律边界条件电阻计算及复习,5,For a homogeneous conducting medium,We know that a curl-free vector field can be expressed as the gradient of a scalar potential field. Let us write,Substitution of this equation into,yields a Laplaces equation in ; that is,电磁场与电磁波第12讲焦耳定律边界条件电阻计算
4、及复习,6,Two fields are found to be very similar in source-free region.,Steady Electric Current Field,Electrostatic Field,The electric current density J corresponds to the electric field intensity E, and the electric current lines to the electric field lines.,In some cases, since the steady electric cu
5、rrent field is easy to be constructed and measured, the electrostatic field can be investigated based on the steady electric current field with the same boundary conditions, and this method is called electrostatic simulation.,电磁场与电磁波第12讲焦耳定律边界条件电阻计算及复习,7,Capacitance,Resistance,Based on the equations
6、 for two fields, we can find the resistance and conductance between two electrodes as,电磁场与电磁波第12讲焦耳定律边界条件电阻计算及复习,8,In certain situations, electrostatic and steady-current problems are not exactly analogous, even when the geometrical configurations are the same. This is because current flow can be co
7、nfined strictly within a conductor (which has a very large in comparison to that of the surrounding medium), whereas electric flux usually cannot be contained within a dielectric slab of finite dimensions. The range of the dielectric constant of available materials is very limited, and the fluxfring
8、ing around conductor edges makes the computation of capacitance less accurate.,电磁场与电磁波第12讲焦耳定律边界条件电阻计算及复习,9,Main topic 恒定电流,3. 电阻的计算,1. 功率耗散和焦耳定律,2. 电流密度的边界条件,电磁场与电磁波第12讲焦耳定律边界条件电阻计算及复习,10,1. 功率耗散和焦耳定律,宏观上，导体中的电子受电场的影响，发生漂移运动；在微观上，这些电子与晶格上的原子发生碰撞。因此，能量从电场传到作热振动的原子上。将电荷移动了一段距离 ，电场E 作的功为q E ，则其所对应的功率为
9、：,其中 u 为漂移速度。传递到体积 dv 内所有电荷载体的总功率为:,电磁场与电磁波第12讲焦耳定律边界条件电阻计算及复习,11,The total electric power converted into heat in volume V:,This is known as Joules law. The point function EJ is a power density under steady-current conditions.,In a conductor of a constant cross section, we can written as,电磁场与电磁波第12讲
10、焦耳定律边界条件电阻计算及复习,12,2. 电流密度的边界条件,When current obliquely crosses an interface between two media with different conductivities(12), the current density vector changes both in direction and in magnitude. A set of boundary conditions can be derived for J in a way similar to that used in Section 3-9 for o
11、btaining the boundary conditions for D and E. The governing equations for steady current density J in the absence of non-conservative energy sources are,电磁场与电磁波第12讲焦耳定律边界条件电阻计算及复习,13,电磁场与电磁波第12讲焦耳定律边界条件电阻计算及复习,14,the normal component of current density vector J being continuous.,the ratio of the tan
12、gential components of current density vector J at two sides of an interface is equal to the ratio of the conductivities.,电磁场与电磁波第12讲焦耳定律边界条件电阻计算及复习,15,When a steady-current flows across the boundary between two different lossy dielectrics:,电磁场与电磁波第12讲焦耳定律边界条件电阻计算及复习,16,For a homogeneous conducting m
13、edium,We know that a curl-free vector field can be expressed as the gradient of a scalar potential field. Let us write,Substitution of this equation into,yields a Laplaces equation in ; that is,电磁场与电磁波第12讲焦耳定律边界条件电阻计算及复习,17,Example 5-4 P214: An emf is applied across a parallel-plate capacitor of are
14、a S. The space between the conductive plates is filled with two different lossy dielectrics of thickness d1 and d2 , permittivities 1 and 2 ,and conductivities 1 and 2 respectively. Determine (a)the current density between the plates, (b)the electric field intensities in both dielectrics, and (c)the
15、 surface charge densities on the plates and at the interface.,电磁场与电磁波第12讲焦耳定律边界条件电阻计算及复习,18,1.,2.,Method one,Or method two,电磁场与电磁波第12讲焦耳定律边界条件电阻计算及复习,19,3.,电磁场与电磁波第12讲焦耳定律边界条件电阻计算及复习,20,1. Choose an appropriate coordinate system for the given geometry. 2. Assume a potential difference V0 between con
16、ductor terminals. 3. Find E from E=-V (2V=0), or other relations. 4. Find the total current where S is the cross-sectional area over which I flows. 5. Find resistance R by taking the ratio V0/I.,The procedure for computing the resistance of a piece of conducting material between specified equipotent
17、ial surfaces (or terminals) is as follows:,3. 电阻计算(Resistance Calculations),电磁场与电磁波第12讲焦耳定律边界条件电阻计算及复习,21,Example 5-6. 一导电材料形状是四分之一的扁平圆垫圈,其均匀厚度为 h ,电导率为 ,垫圈内半径为 a ,外半径b, 如下图所示,求端面之间的电阻.,思路,电磁场与电磁波第12讲焦耳定律边界条件电阻计算及复习,22,Solution: The cylindrical coordinate system should be selected. Assume the electr
18、ic potential difference between two end faces is V0 , and let,Since the electric potential V is related to the angle , it should satisfy the following equation,The general solution is,The electric potential at,The electric potential at,电磁场与电磁波第12讲焦耳定律边界条件电阻计算及复习,23,Based on the given boundary condit
19、ions, we find,The current density J in the conducting medium is,Then the current I flowing into the conducting medium across the end face at is,Consequently, the resistance R between two end faces is,电磁场与电磁波第12讲焦耳定律边界条件电阻计算及复习,24,summary,1. Power Dissipation and Joules Law,3. Resistance Calculations
20、,electrostatic simulation,电磁场与电磁波第12讲焦耳定律边界条件电阻计算及复习,25,2. Boundary Conditions for Current Density,When a steady-current flows across the boundary between two different lossy dielectrics:,电磁场与电磁波第12讲焦耳定律边界条件电阻计算及复习,26,homework,Thank you! Bye-bye!,答疑安排 时间： 地点：1401， 1403,P.5-15,电磁场与电磁波第12讲焦耳定律边界条件电阻计算
21、及复习,27,1. Current Density and Ohms Law,Review Steady Electric Currents,电磁场与电磁波第12讲焦耳定律边界条件电阻计算及复习,28,3. Equation of Continuity and Kirchhoffs Current Law,2. Electromotive Force and Kirchhoffs Voltage Law,电磁场与电磁波第12讲焦耳定律边界条件电阻计算及复习,29,4. Power Dissipation and Joules Law,6. Resistance Calculations,electrostatic simulation,电磁场与电磁波第12讲焦耳定律边界条件电阻计算及复习,30,5. Boundary Conditions for Current Density,When a steady-current flows across the boundary between two different lossy dielectrics:,电磁场与电磁波第12讲焦耳定律边界条件电阻计算及复习,31,电磁场与电磁波第12讲焦耳定律边界条件电阻计算及复习,32,电磁场与电磁波第12讲焦耳定律边界条件电阻计算及复习,33,