电磁场与电磁波第15讲边界条件电感磁能.ppt

* Field and Wave Electromagnetic 电磁场与电磁波 2014. 4.7 1. The Magnetic Dipole 2. Magnetization and Equivalent Current Densities Review 3. Magnetic Field Intensity and Relative Permeability Differential form Integral form Postulates of Magnetostatics in magnetic material Main topic 静磁场 1. 静磁场的边界条件 2. 电感和电感器 3. 静磁场能量 1. 静磁场的边界条件 ?1 ?2 B2 H1 B1 H2 an2 Js E2 E1 ? 2 ? 1 at ?w ?h a c d b an2 ?h ?S ? 2 ? 1 an2 D1 D2 ?s (a) 在分界面处B的法向分量是连续的. For linear isotropic media, we have (b) 磁场H 的切向分量在跨越存在面电流的分界面时,是不连续的. 在跨越几乎所有物理媒质的边界时, H 的切向分量都是连续的; 只有当分界面为理想导体或超导体时,它才不连续. Example 1. A loop magnetic core with a gap is closely wound by a coil with N turns, as shown in the figure. When the coil carries a current I, and the leakage magnetic flux outside the coil is neglected, find the magnetic flux density and the magnetic field intensity in the core and the gap. Solution: Since the leakage magnetic flux is neglected, the direction of the magnetic flux density is around the circle, and it is perpendicular to the end faces of the gap. From the boundary condition, we know that the magnetic flux density Bg in the gap is equal to Bf in the core, i.e. Since r0 a , the magnetic field in the core can be considered to be uniform. Using Ampere’s circuital law in media, and taking the circle of radius r0 as the integral path, then we have Considering , we have Then In the gap In the core 2. 电感和电感器 互磁通?12 (Mutual flux) Faraday’s law of electromagnetic induction Biot-Savart law 其中,比例系数 L12 称为回路C1 和 C2之间的互感, with the unit henry (H). In case C2 has N2 turns, the flux linkage ?12 (磁链数)due to ?12 由上式,两个电路之间的互感是一电路通以单位电流时,另一电路所交链的磁通链. 这个关系只适用于线性媒质. L12 更一般的定义为: I1 所产生的某些磁通量只与回路 C1 自身交链,而不与 C2交链.the total flux linkage (磁链数) with C1 caused by I1 is Neumann formula 回路 C1 的自感定义为在回路本身通以单位电流时所产生的磁链,即: 对线性媒质而言,更一般的表达式 L11 为: 一个回路或电路的自感,取决于构成这个回路或电路的导体的几何形状和物理排列以及媒质的磁导率.在线性媒质中,自感与回路或电路的电流无关.事实上,无论回路或电路是开路还是闭合的,也无论它是否靠近另一回路或电路,其自感总是存在的. 排列成适当形状(例如由导线缠绕而成的