Electric field and potential distribution in the surroundings of cube electrodes are numerically determined using Equivalent Electrodes Method

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A new theoretical approach to the problem of the symmetrical linear antenna driven by a two-wire line is presented. Then symmetrical linear antenna and the feeder line are treated as a unique boundary-value problem leading to a system of two simultaneous integral equations containing antenna and line currents as unknown sub-integral functions. The integral equations are approximately solved by the so-called point-matching method. Due to the mutual coupling between the antenna and the line, a new conveniently defined apparent driving-point admittance is to be introduced. The method is applied on several types of linear antennas: Centre driven symmetrical dipole antenna, Centre-driven V-antenna, Cage antenna, H-antenna and System of two parallel non-staggered dipoles antennas, positioned in the air over semi-conducting ground. Then theoretical results for admittances were compared with the experiments and remarkably good overall agreement has been found. On the contrary, a comparison with the corresponding theoretical results obtained with the idealized delta-function generator revealed remarkable discrepancies

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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.