北京理工大学电场Ch.1.ppt

Boundary Conditions For problem involving contiguous regions of different ? ?, we need to know the boundary conditions: From the integral forms of Maxwell’s equations, we get For tangential components, For normal components medium 1 medium 2 From Maxwell’s equations: (1) Faraday’s Law When w tends to 0, E1t=E2t Tangential E-field is continuous across an interface E1 E2 E3 E4 w l medium 1 medium 2 y x z From Maxwell’s equations: (2) Ampere’s Law When w tends to 0, Jzw ? Js , Ht2 – Ht1 = Js Tangential H-field is discontinuous across an interface where a free surface current exists H1 H2 H3 H4 w l medium 1 medium 2 y x z From Maxwell’s equations: (3) Gauss’s Law Normal component of D field is discontinuous across an interface where a surface charge exists. The amount of discontinuity being equal to the surface charge density D1 D2 medium 1 medium 2 From Maxwell’s equations: (4) Normal component of B field is continuous across an interface B1 B2 medium 1 medium 2 Interface between 2 lossless linear media No free charges and no surface currents at interface between two lossless media Interface between a dielectric and a perfect conductor Special Cases In solving field problems, good conductors are often considered as perfect conductors in regard to boundary conditions. * The charges can only reside on the surface. Conductivities of materials (?) silver, copper, gold, aluminum, brass, iron Interior of a perfect conductor, E = 0 ( otherwise J = ?E ?). Therefore, D=0 Interrelationship between (E, D) and (B, H) from Maxwell’s, B=H=0 Interface between a dielectric and a perfect conductor Medium 1 Medium 2 1 2 2 perfect 1 dielectric conductor 1 2 + + + + + + + + + + Interface between a dielectric and a perfect conductor Determined Formulation of Electromagnetic Problems Maxwell’s Equations Constitutive Relations Boundary Conditions Electrostatic Problems Electromagnetic field is invariant with time