Lecture ( 9 ) Chapter Three : Electric Field in Material Space

Transcription

1 Lecture ( 9 ) Chapter Three : Electric Field in Material Space Properties of Materials, Convection and Conduction Currents, and Conductors 3.1 Properties of Materials Just as electric fields can exist in free space, they can exist in material media. Materials are broadly classified in terms of their electrical properties as conductors, semiconductors and insulators. Non-conducting materials are usually referred to as insulators or dielectrics. A conductor is a material which contains movable electric charges. Metals such as copper aluminium are examples of conductors. In a Conductor the outer electrons of the atoms are loosely bound and free to move through the material. In conductors, the valence electrons are essentially free and strongly repel each other. Any external influence which moves one of them will cause a repulsion of other electrons which propagates through the conductor. In an insulator the free electric charges are very few in number. Most solid materials are classified as insulators because they offer very large resistance to the flow of electric current. In insulators the outermost electrons are so tightly bound that there is essentially zero electron flow through them with ordinary voltages. The properties of semiconductors lie in between conductors and insulators. Here we examine the electric field inside a conductor and an insulator. Also is Classified in terms of their conductivity High conductivity ( >> 1) is referred to as a metal Low conductivity (<< 1) is referred to as a dielectrics (or insulators) The rest is semiconductor Note: the major difference between a metal and dielectric lies in the amount of electrons available for conduction of current 3.2 Convection and Conduction Currents The current density ( J ) = =.

2 = Current classification: 1. Conduction current is the current flowing through a conductor 2. Convection current is the current flowing through an insulating medium (doesn t satisfy Ohm s law) 3. Displacement current Convection current, as distinct from conduction current, dose not involve conductors and consequently does not satisfy Ohm s law A flow charge (, ) The y- direction current density ( J y ) is given point is the current through a unit normal area at that point by Hence, in general ( J Convection current density ( A / m 2 ) ) Conduction current, requires a conductor. A conductor is characterized by a large amount of free electrons that provide conduction current due an impressed electric field y

3 The force on an electron with charge ( -e ) is According to Newton s law, we have F = -ee Where ( τ ) is the average time interval between collisions, if there are ( n ) electrons per unit volume, the electron charge density is given by Thus the conduction current density is = = = = = The conductivity of the conductor ( σ ) 3.3 Conductors A perfect conductor cannot contain an electrostatic field with it, under static conditions

4 Surface charge The induced Very quickly An isolated conductor under the influence of a static electric field A conductor has zero electric field under static conditions Resistance As the electrons move, they encounter some damping forces called resistance as shown in figure S A conductor of uniform cross section under an applied ( E ) field The electric field applied is uniform and its magnitude is given by Since the conductor has a uniform cross section

5 Substituting ( J = σ E ) and use the value of ( E ) we obtain Hence or Where ( = )is the resistivity of the material The basic definition of resistance ( R ) as the ratio of the potential difference ( V ) between the two ends of the conductor to the current ( I ) through the conductor still applies Power ( P ) Power P (in watts) is define as the rate of change of energy W (in joules) or force times velocity P = F.u =. =. Or =. For a conductor with uniform cross section, dv = ds dl, so last equation becomes = =

6 Or =