Low Frequencies Electromagnetic Field Analysis In Bianisotropic Media

Abstract

The bianisotropic media, magnetoelectric materials, having constitutive relations D = E E + x H and B = p H + x E (vector values are in bold) are theoretically predicted by Dzyaloscinskii (1959) and by Landau and Lifshitz (1957) and experimentally observed by Astrov in chromium oxide (1 960) [I] . The present paper shows a general procedure for low frequency (LF) electromagnetic (EM) field determination in bianisotropic media. Using Maxwell's equations: rot H = J , rot E = O , divD = p and divB =0, the following two independent excitation cases are observed: a) Electrostatic problems, where p # 0 and J = 0 ( p is the volume charge density and J is electric current density ) Introducing scalar potential functions, electric, 9, and magnetic, 9 , , scalar potential, the electric, E, and magnetic, H, field strength are defined as: E = -g r a d 9 and H=-grad qm ,whereAcp=-pl& ,AV,,,= X p / p E e a n d E e = & -X 2 / p . If Q is electric scalar potential in free space, A$ = -p / EO, then: cp = q Q I Ee and cp, = -x Q I p . Finally, E = E O E O / E~, Eo=-grad~$ , H = -x E / p , D = E~E and B=O. b) If p = 0, but LF current exists, J# 0, it is convenient to use vector potential functions, magnetic, A, and electric, F, vector potential.Then magnetic flux density, B, and electric displacement, D, are: B = r o t A and D = r o t F, where A A = -p J and A F = -x J. Vector potentials satisfy gauge conditions : div A = 0 and div F = 0 [2] IfA is free space solution, AA = -p~ J , then : In order to illustrate the present procedure several examples are used. 1) For isolated point charge, q, placed in coordinate origin: where r is radius vector of field point. 2) For isolated linear conductor having LF current I and infinite length ( L + m ) and placed on direction r = 0 : A 3) Bianisotropic spherical body with radius a in homogeneous magnetic field Ho = X -b z . Outside the body is free space. Using scalar potential functions and solving Laplace's equation by method of separation of variables with boundary conditions on the body surface that tangential components of electric and magnetic field strengths and normal components of magnetic flux density and electric displacement are unchanged, the potential scalar functions are C l r c o s e r s a CZrcosf3 r S a .={ C 3 c o s e / r 2 r > a and vm={-Ho r Wse + c4 case / r2 r 2 a , where C1= 3p,,x&/ 6 , C2 = -3p,,(~+2~0)Ho 1 6 , C3 = 3p,,xa3Ho/6, C4 = ~~H~[(E+~Eo)(~-I.Io)] 1 6 , 4) Infinite linear conductor with LF current I above bianisotropic half space (Fig.). 6 = (€+2Eo)(p+2I.IO) -x 2 . region 1 region 2 -C2 In r2 in 2 -C3ln rz in 1 -C3 In rl in 2 ' F ={ bianisotropic media Using integral transform method and satisfying all boundary conditions, the vector potential axial components are (all infinite components are ignored) :References:The obtained results give image theorem.

Quasi-static analysis of the shielded microstrip line with bi-isotropic substrate by the strong FEM formulation

“…In [6] the effects of anisotropy were analyzed in some detail. In [7][8][9] the effect of the Tellegen's bi-isotropy in electrostatic problems was studied and quasi-static analysis performed by the Equivalent Electrode Method (EEM) [10]. In [11] the effects of bi-isotropy of the Tellegen's type were analyzed using weak FEM formulation and quasi-static approach.…”