ANALYSIS OF THE FIELDS FROM HERTZIAN DIPOLE IN AN INFINITE HOMOGENOUS MEDIUM Eftim ZDRAVEVSKI 1 , Vesna ARNAUTOVSKI-TOSEVA 2 and Leonid GRCEV 3 1 Faculty of electrical engineering, University Saints Cyril and Methodius, Skopje, 1000 Karpos II bb, Macedonia, E-mail: zeftim@yahoo.com 2 Faculty of electrical engineering, University Saints Cyril and Methodius, Skopje, 1000 Karpos II bb, Macedonia, E-mail: atvesna@etf.ukim.edu.mk 3 Faculty of electrical engineering, University Saints Cyril and Methodius, Skopje, 1000 Karpos II bb, Macedonia, E-mail: lgrcev@etf.ukim.edu.mk Abstract: This paper presents the analysis of harmonic electric and magnetic fields from Herzian dipole in homogenous infinite space. The main objective of this study is to investigate the behavior of the components of electric and magnetic fields with respect to distance to the observation point. In addition, the real part of the complex Poynting vector was analysed in order to have information about the power flow. Some preliminary results are presented. Keywords: Electromagnetic analysis, Electric and magnetic fields, Poynting vector. INTRODUCTION The Hertzian dipole – also called a current element or electric dipole is an elementary source which is assumed as a basic conceptual tool for analysing the electromagnetic fields. It is assumed to consist of a time- varying point current with equal and opposite time- varying point charges on either end, which follows from the conservation of charge. The fields of a Hertzian dipole are usually derived in the literature by using the electromagnetic approach which involves scalar and vector potentials and Maxwell equations [1]. In the paper, Coulomb’s law and Biot-Savart law are extended to include the time-varying point sources that make up a Hertzian dipole. The theoretical approach is based on the physical origins of the elementary components, point current and point charges and their electric and magnetic component fields given in [2]. FIELDS OF A HERTZIAN DIPOLE For a Hertzian dipole in an infinite homogenous free space centred in the spherical coordinate system in positive direction θ = 0 (as shown on Fig. 1), the electric and magnetic fields are defined as follows [1] 2 sin ( ) () ( ) 4 r it rc H t it rc c t r φ θ π ∂ −   = − +   ∂   l , (1) 0 2 sin ( ) () [ ( ) 4 ( ) ] c qt rc E t Z qt rc r t r r it rc c t θ θ π ∂ − = − + + ∂ ∂ − ∂ l , (2) 0 2 cos ( ) () [ ( ) ] 2 r c qt rc E t Z qt rc r t r θ π ∂ − = − + ∂ l (3) Fig.1 – A Hertzian dipole and its fields. where c is the free space propagation velocity of electric and magnetic waves, ε 0 and µ 0 are the permittivity and permeability, and Z 0 is the free space characteristic impedance 0 0 0 Z µ ε = . (4) FIELDS OF A POINT CURRENT A point current is defined as the electric current at any chosen point in a circuit, or on an antenna. For a point of time-constant current I with length ℓ → 0, the Biot-Savart law says that, at any distance r it causes the magnetic field 2 sin 4 H I r φ θ π = l . (5) From Eq. (1), it may be concluded that the first component of H φ (t) follows directly from the Biot-Savart law when the current is assumed to be time-varying, I → i(t) with free space propagation delay included 2 sin () ( ) 4 I H t it rc r φ θ π = − l , (6) which is also called the induction field component, wherefrom its notation H φ I (t). The second component of H φ(t) in Eq. (1), is radiated field component that accounts for the current derivative di(t)/dt which also increases and decreases as the point current increases and decreases, with free space propagation delay included. According to [2], the coefficient r/c of the second component establishes the appropriate units for that component, and it also establishes the appropriate predominance for both components when r → ∞ and when r → 0. i(t) +q(t) -q(t) E r (t) E θ(t) r θ ℓ→0 H φ(t) i(t) E θ r θ ℓ→ H φ I (t) + H φ R (t) ℓ→