Boundary Conditions for Time Varying Fields

Boundary Conditions for Time Varying Fields

AU : Dec.-03

• The relationship between the electric flux density  , electric field intensity   magnetic flux density   and magnetic field intensity  can be explained with the help of the point form or the integral form of Maxwell's equations. The field equations postulated by Maxwell are valid at a point in a continuous medium. The Maxwell's equations are useful in determining the conditions at the boundary surface of the two different media. We can apply the concepts of linear, isotropic and homogeneous medium. Consider the boundary between medium 1 with parameters Ɛ₁,µ₁ and σ₁  and medium 2 with parameters Ɛ₂,µ₂ and σ₂. In general, the boundary conditions for time varying fields are same as those for static fields. Thus at the boundary, refering boundary conditions for static electric magnetic fields, we can write,

i) The tangential component of electric field intensity  is continuous at the surface.

E_tan1 = Et_an2  ….. (9.6.1)

ii) The tangential component of the magnetic field intensity is continuous across the surface except for a perfect conductor.

H_tan1 = Ht_an2 ….. (9.6.2)

• At the surface of the perfect conductor, the tangential component of the magnetic field intensity is discontinuous at the boundary.

H_tan1 = Ht_an2  = K

iii) The normal component of the electric flux density is continuous at the boundary if the surface charge density is zero.

D_N1 = D_N2

• If the surface charge density is non zero, then the normal component of the electric flux density is discontinuous at the boundary.

DN1 - D_N2 = ρS   ...(9.6.3(a))

iv) The normal component of the magnetic flux density is continuous at the boundary.

B_N1 = B_N2 ..... (9.6.4)

Review Questions

1. What are the general statements about electromagnetic boundary conditions ?

2. Write down the boundary conditions between a dielectric (medium 1) and a perfect conductor (medium 2) for time varying case.

3. State the boundary conditions of time varying fields at the interface between two dielectric media and between a dielectric medium and a perfect metal.