电磁场与电磁波第14讲边界条件电感磁能-wb要点解析.ppt

* Field and Wave Electromagnetics 电磁场与电磁波 2012. 4. 6 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 Steady Magnetic Fields 1. Boundary Conditions for Magnetostaic Fields 2. Inductances and Inductors 3. Magnetic Energy 1. Boundary Conditions for Magnetostaic Fields ?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) The normal components of the magnetic flux density are continuous across an interface. For linear isotropic media, we have (b) The tangential component of the H field is discontinuous across an interface where a free surface current exists The tangential component of H is continuous (连续) across the boundary of almost all physical media; it is discontinuous(不连续) only when an interface with an ideal perfect conductor(理想导体) or a superconductor(超导体) is assumed. 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. Inductances and Inductors Mutual flux ?12 (互磁通) Faraday’s law of electromagnetic induction Biot-Savart law where the proportionality constant L1