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MAHATMA GANDHI INSTITUTE OF TECHNICAL EDUCATION & RESEARCH CENTRE Sub:Engineering Electromagnetic BE 3rd year sem v Electronics &communication Guided by:Sapna garde Anita patel Prepaired by:Pokia Fenil 130330111035 Tiwari shiva 130330111049 Vaghasiya Suraj 130330111051 TOPIC: Nature of dielectric material and boundary condition for perfect dielectric and boundary condition for conductor-free space Dielectric Materials Dielectric materials are also called as insulators. In dielectric materials, all the electrons are tightly bound to their parent molecules and there are no free charges. In addition, the forbidden energy band gap (e.g.) for dielectric materials is more than 3eV. Not possible for the electrons in the valence band to excite to the conduction band, by crossing the energy gap, even with normal voltage or thermal energy. Dielectrics are non-metallic materials of high specific resistance and negative temperature coefficient of resistance Active and Passive Dielectrics The dielectric materials can be classified into active and passive dielectric materials. i. Active dielectrics When a dielectric material is kept in an external electric field, if it actively accepts the electricity, then it is known as active dielectric material. Thus, active dielectrics are the dielectrics, which can easily adapt themselves to store the electrical energy in it. ii. Passive dielectrics Passive dielectrics are the dielectrics, which restrict the flow of electrical energy in them. So, these dielectrics act as insulators. Examples: All insulating materials such as glass, mica, rubber etc., Basic Definitions in Dielectrics Electric Field The region around the charge within which its effect is felt or experienced is known as electric field. The electric field is assumed to consist of imaginary electric lines of force. These lines of force originate from the positive charges and terminate to the negative charges . Electric field strength or electric field intensity (E) Electric field strength at any point is defined as the force experienced by an unit positive charge placed at the point. It is denoted by ‘E’. ‘q’ - magnitude of the charge in coulombs ‘f’ - force experienced by that charge in Newton, electric field strength (E) . Its unit is Newton / Coulomb (or) volt / metre. Electric flux It is defined as the total number of electric lines of force passing through a given area in the electric field. (Emanated from the positive charge). Unit: Coulomb Electric flux density or electric displacement vector (D) It is defined as the number of electric lines of force passing normally through an unit area of cross section in the field. Its unit is Coulomb / m2 Permittivity Permittivity is defined as the ratio of electric displacement vector (D) in a dielectric medium to the applied electric field strength (E). Mathematically the permittivity is, .Its unit is Farad /metre The permittivity indicates the degree to which the medium can resist the flow of electric charge and is always greater than unity. Dielectric Constant The dielectric constant or relative permittivity of a material determines its dielectric characteristics. It is the ratio of the permittivity of the medium and the permittivity of free space Electric Polarization Consider an atom. We know that it is electrically neutral. Furthermore, the centre of the negative charge of the electrons coincides with the positive nuclear charge, which means that the atom has no net dipole moment. However, when this atom is placed in an external electric field, the centre of the positive charge is displaced along the field direction while the centre of the negative charge is displaced in the opposite direction. When a dielectric material is placed inside an electric field, such dipoles are created in all the atoms inside. Polarizability () When the electric field strength ‘E’ is increased, the strength of the induced dipole is also increased. Thus, the induced dipole moment is proportional to the intensity of the electric field. Polarization vector The dipole moment per unit volume of the dielectric material is called polarization vector. ’ - average dswdipole moment per molecule and ‘N’ - number of molecules per unit volume Unit: Coulomb / m2 Polarization vector is given by, CONDUCTOR CONDITIONS – FREE + + + + + + + SPACE BOUNDARY free space conductor - - - - - - - GRAPHICAL ILLUSTRATION E1t E1n E1 Medium # 1 Medium # 2 E2n E2 E2t E1 E 2 E1t + E1n Normal component Tangential component E2n + E2t NORMAL COMPONENTS E1n 1 E1n S Maxwell’s equation (Gauss’s law) rs #1 + E2n + + #2 2 + h 3 E2n D ds Qen D 1 n ẑ s 0 D ds1 D ds 2 D ds 3 ds 1 ẑ D 2 n ẑ r ds s ds3 ẑ Assume h → 0 Boundary condition for normal components D1n S D2 n S rs S D1n D2 n rs s TANGENTIAL COMPONENTS E1t #1 1 E1t 2 Maxwell’s equation (Conservation of energy) h #2 4 E2t E d 0 3 ℓ E2t 0 0 3 4 1 2 E d E d E d E d 1 2 3 4 Assume again h → 0 Boundary condition for tangential components E1t E2 t E1t E2 t 0 CONDUCTOR – FREE SPACE BOUNDARY CONDITION #1 Free space e0 #2 Conductor e0 Boundary condition for normal components 0 D1n D2 n rs Boundary condition for tangential components 0 E1t E2 t D1n rs Boundary conditions for conductor – free space/dielectric E1 t E 2 t 0 GRAPHICAL ILLUSTRATION Conductor Free space + + + Unit vector normal to the surface + + + D rsân + + rs rs E â n e0 SUMMARIZED THE PRINCIPLES WHICH APPLY TO CONDUCTORS IN ELECTROSTATIC FIELDS The static electric field intensity inside a conductor is zero. The static electric field at the surface of a conductor is everywhere directed normal to that surface. The conductor surface is an equipotential surface.