1 Electromagnetics I EELE 3331 Dr Assad AbuJasser
1 Electromagnetics I (EELE 3331) Dr. Assad Abu-Jasser - EE Department - IUGaza Electromagnetics I
2 Assad Abu-Jasser, Ph. D Electric Power Engineering The Islamic University of Gaza ajasser@iugaza. edu. ps site. iugaza. edu. ps/ajasser Dr. Assad Abu-Jasser - EE Department - IUGaza Electromagnetics I
3 Chapter 5 Electric Fields in Material Space Dr. Assad Abu-Jasser - EE Department - IUGaza Electromagnetics I
4 Introduction Electrostatic fields in free space (vacuum) were considered in chapter 4 This chapter covers theory of electric phenomena in material space Materials are broadly classified as conductors and nonconductors Nonconducting materials are usually referred to as insulators or dielectrics Dr. Assad Abu-Jasser - EE Department - IUGaza Electromagnetics I
5 Properties Of Materials classified in terms of their conductivity σ, in mohs per meter (Ʊ/m), or siemens per meter (S/m) Materials with high conductivity are referred to as metals, and those with low conductivity referred to as insulators Materials with conductivity that lies somewhere between those of metals and insulators are called semiconductors Dr. Assad Abu-Jasser - EE Department - IUGaza Electromagnetics I
6 Electric Current Electric current is generally caused by the motion of electric charges The current (in amperes) through a given area is the electric charge passing through In a current of one ampere, the area per unit time charge is being transferred at a rate of one coulomb per second Dr. Assad Abu-Jasser - EE Department - IUGaza Electromagnetics I
7 Convection Current Convection current does not involve conductors and does not satisfy Ohm’s law v It occurs when current flows through y insulating medium such as liquid, vacuum ρ ≡ density u ≡ velocit The current density at a given point is the current through a unit normal area at that point Dr. Assad Abu-Jasser - EE Department - IUGaza Electromagnetics I
8 Conduction Currents Conduction current require a conductor A conductor has a large number of free electrons that establish conduction current when electric field is impressed Dr. Assad Abu-Jasser - EE Department - IUGaza Electromagnetics I
9 Conductors When external field Ee applied, positive free A conductor hasalong an abundance charges pushed same fieldofdirection, that is free to move negative charges move in opposite direction ACharge perfectmigration conductortakes (σ=∞)place cannot contain an very quickly electrostatic field within it Free charges accumulate on the surface and A conductor is called equipotential body, form an induced surface charge potential same charges everywhere in the conductor The induced set internal field Ei that cancels the external applied field Dr. Assad Abu-Jasser - EE Department - IUGaza Electromagnetics I
10 Example 5. 1 If J=(1/r 3)(2 cosθ ar+sinθ aθ) A/m 2, calculate the current passing through a) A hemispherical shell of radius 20 cm, 0<θ<π/2, 0<φ<2π b) A spherical shell of radius 10 cm Dr. Assad Abu-Jasser - EE Department - IUGaza Electromagnetics I
11 Example 5. 2 A typical example of convective charge transport is found in the Van Graaf generator where charge is transported on a moving belt from the base to the dome as shown. If the surface charge density 10 -7 C/m 2 is transported by the belt at a velocity of 2 m/s, calculate the charge collected in 5 s. take the width of the belt as 10 cm. Dr. Assad Abu-Jasser - EE Department - IUGaza Electromagnetics I
12 Example 5. 3 A wire of diameter 1 mm and conductivity 5 x 107 S/m has 1029 free electrons per cubic meter when an electric field of 10 m. V/m is applied. Determine a) The charge density of free electrons b) The current density c) The current in the wire d) The drift velocity of the electrons (take the electron charge as e=-1. 6 x 10 -19 C) Dr. Assad Abu-Jasser - EE Department - IUGaza Electromagnetics I
13 Example 5. 4 A lead (σ=5 x 106 S/m) bar of square cross section has a hole along its length of 4 m so that its cross section becomes that as shown. Find the resistance between the square ends. Dr. Assad Abu-Jasser - EE Department - IUGaza Electromagnetics I
14 Polarization in Dielectrics Consider an atom of the dielectric consisting of a negative charge –Q (electron cloud) and a positive charge +Q (nucleus) Similar picture can be adopted for a dielectric molecule; nuclei treated as point The previous type of dielectric is said to be nonpolar, charge and electronic structure as single negative cloud oxygen, and rarethe gases We havehydrogen, equal amounts of positivenitrogen, and negative charge, whole atom or Dielectric material molecule is electrically neutral Nonpolar dielectric molecules do not posses dipoles until With field E, the positive charge is displacedconsisting in direction ofof E by force F +=QE, dipoles with the application of the electric field while negative charge is displace in opposite direction by the force F -=QE dipole moment P diploes per unit typesfrom of dielectrics have built-in permanent AOther dipole results the displacement of charges, and the dielectric is said to volume polarized randomly oriented andbesaid to be polar such as water, In polarized state, the distorted charge distribution is equivalent to the original sulfurdistribution dioxide, plus hydrochloric acid, and polystyrene a dipole whose momentum is p=Qd When field is applied, the random dipoles experience a torque tending to align them with the field Dr. Assad Abu-Jasser - EE Department - IUGaza Electromagnetics I
15 Dielectric Constant ε permittivity of dielectric εo Permittivity free space εr relative permittivity Dielectric constant (relative permittivity) εr is the ratio of the permittivity of the dielectric to that of free space Dr. Assad Abu-Jasser - EE Department - IUGaza Electromagnetics I
16 Dielectric Strength There is no ideal dielectric When electric field is sufficiently large, it pulls electrons completely out of molecules and it becomes conducting Dielectric breakdown occurs in all kinds of dielectric materials and depends on many factors Dielectric strength is the minimum value of electric field at which dielectric breakdown occurs Dr. Assad Abu-Jasser - EE Department - IUGaza Electromagnetics I
17 Dielectrics Linear, Homogeneous, and Isotropic A dielectric material is linear if D=εE and ε does not change with the applied E field A material is linear if D varies linearly with E A dielectric material is homogenous if D=εE and Homogenous materials are those for which ε or σ ε does not change from point to point does not vary in the region being considered A inhomogeneous dielectric material is isotropic if D=εE and εε In (nonhomogenous) materials does not change with direction is dependent on the space coordinates Isotropic arefor those for whichmaterials D and E are The samematerials idea holds conducting in in the same which J=σEdirection applies. In anisotropic (nonisotropic) E, and Linear materials, σ doesmaterials not vary D, with E P are not parallel ε has components Homogenous, σ is the nine same at all points Isotropic, σ does not vary with direction Dr. Assad Abu-Jasser - EE Department - IUGaza Electromagnetics I
18 Example 5. 5 A dielectric cube of side L and center at the origin has a radial polarization given by P= ar, where a is a constant and r=xax+yay+zaz. Find all bound charge densities and show explicitly that the total bound charge vanishes. Dr. Assad Abu-Jasser - EE Department - IUGaza Electromagnetics I
19 Example 5. 6 The electric field intensity in polystyrene (εr=2. 55) filling the space between the plates of parallel-plate capacitor is 10 k. V/m. The distance between the plates is 1. 5 mm. calculate a) D b) P c) The surface charge density of free charge on the plates d) The surface density polarization charge e) The potential difference between the plates Dr. Assad Abu-Jasser - EE Department - IUGaza Electromagnetics I
20 Example 5. 7 A dielectric sphere (εr=5. 7) of radius 10 cm has a point charge of 2 p. C placed at its center. Calculate a) The surface density of polarization charge on the surface of the sphere b) The force exerted by the charge on a -4 p. C point charge placed on the sphere Dr. Assad Abu-Jasser - EE Department - IUGaza Electromagnetics I
21 Example 5. 8 Find the force with which the plates of a parallel-plate capacitor attract each other. Also determine the pressure on the surface of the plate due to the field Dr. Assad Abu-Jasser - EE Department - IUGaza Electromagnetics I
22 Continuity Equation and Relaxation Time Principle of Charge Conservation Relaxation Time (T ) r The time rate of decrease of charge within a given The time it takes charge placed in the interior of a volume must beaequal to the net outward current -1 (36. 8%) of its initial value material to drop to e flow through the surface of the volume Dr. Assad Abu-Jasser - EE Department - IUGaza Electromagnetics I
23 Boundary Conditions So far, electric field in homogeneous medium has been considered For fieldconditions in region consisting two different Boundary applied toof find electric field media, the given conditions that must beboundary satisfied are on one side field on the other side called boundary condition Boundary conditions used to determine refraction • Dielectric (εr 1) and dielectric of field across the interface(εr 2) • Conductor and dielectric • Conductor and free space Dr. Assad Abu-Jasser - EE Department - IUGaza Electromagnetics I
24 Boundary Conditions Dielectric-Dielectric Boundary conditions applied to find electric field on one side given field on the other boundary side Boundary conditions used to determine refraction of field across the interface Dr. Assad Abu-Jasser - EE Department - IUGaza Electromagnetics I
25 Boundary Conditions Conductor-Dielectric An application for E=0 inside a conductor is in electrostatic screening or shielding Dr. Assad Abu-Jasser - EE Department - IUGaza Electromagnetics I
26 Boundary Conditions Conductor-Free Space This is a special case of a conductor-dielectric boundary condition, where the relative permittivity of the free space εr is taken as 1 The electric field E must be external to the conductor and normal to its surface Dr. Assad Abu-Jasser - EE Department - IUGaza Electromagnetics I
27 Example 5. 9 Two extensive homogeneous isotropic dielectrics meet on plane z=0. for z>0, εr 1=4 and for z<0, εr 2=3. A uniform electric field E 1=5 ax-2 ay+3 az k. V/m for z≥ 0. Find (a) E 2 for z≤ 0 (b) the angle E 1 and E 2 make with the interface (c) the energy densities (in J/m 3) in both dielectrics (d) the energy within a cube of side 2 m centered at (3, 4, -5) Dr. Assad Abu-Jasser - EE Department - IUGaza Electromagnetics I
28 Example 5. 10 Region y<0 consists of a perfect conductor while region y>0 is a dielectric medium (εr=2). If there is a surface charge of 2 n. C/m 2 on the conductor, determine E and D at (a) A(3, -2, 2) (b) B(-4, 1, 5) Dr. Assad Abu-Jasser - EE Department - IUGaza Electromagnetics I
29 End Of Chapter Five Dr. Assad Abu-Jasser - EE Department - IUGaza Electromagnetics I
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