목원대학교 전자정보통신공학부 전자기학 5-1 Chapter 5. Conductors, Dielectrics, and Capacitance 1.Current and Current Density Current(A) : a rate of movement of charge passing a given reference point (or crossing a reference plane).

목원대학교 전자정보통신공학부 전자기학 Continuity of Current The principle of conservation of charge: charges can be neither created nor destroyed. The current, or charge per second, diverging from a small closed surface per unit volume is equal to the time rate of decrease of charges per unit volume at every point. A numerical example: p. 123

목원대학교 전자정보통신공학부 전자기학 Metallic Conductors

목원대학교 전자정보통신공학부 전자기학 5-4 The point form of Ohm ’ s law Isotropic: same properties in every direction Anisotropic: not isotropic Resistivity: reciprocal of the conductivity Superconductivity: the resistivity drops abruptly to zero at a few kelvin Higher temperature→greater crystalline lattice vibration→lower drift velocity →lower mobility →lower conductivity →higher resistivity

목원대학교 전자정보통신공학부 전자기학 Conductor Properties and Boundary Conditions Suppose that there suddenly appear electrons in the interior of a conductor→Electric fields by these electrons →The electrons begin to accelerate away from each other →The electrons reach the surface of the conductor Good conductor: zero charge density within a conductor and a surface charge density resides on the exterior surface No charge, no electric field within a conducting material  Relate external fields to the charge on the surface of the conductor The external electric field intensity is decomposed into tangential component and normal component to the conductor surface. Static condition: tangential one may be zero. If not, there will result in a movement of electrons.

목원대학교 전자정보통신공학부 전자기학 5-6  Guass ’ s law: The electric flux leaving a small increment of surface must be equal to the charge residing on that incremental surface. The flux must leave the surface normally! The flux density per square meter leaving the surface normally is equal to the surface charge density per square meter

목원대학교 전자정보통신공학부 전자기학 5-7 Boundary conditions for the conductor-free space boundary in electrostatics Summary: p The Method of Images The dipole field: the infinite plane at zero potential that exists midway between the two charges. Remove conducting plane and locating a negative charge (image)

목원대학교 전자정보통신공학부 전자기학 5-8  Semiconductors Current carriers: electrons (conduction band), holes (valence band) Temperature↑: mobility↓, charge density ↑(more rapidly)  Conductivity ↑ Doping Donors: additional electrons, n-type Acceptors: extra holes, p-type

목원대학교 전자정보통신공학부 전자기학 The Nature of Dielectric Materials Bound charges: bound in place by atomic and molecular forces. Only shift positions slightly in response to external fields. Dielectric materials can store electric energy (a shift in the relative positions of the internal, bound positive and negative charges against the normal molecular and atomic forces) Polar molecule: random dipole → alignment Nonpolar molecule: dipole arrangement after a field is applied Define: Polarization as the dipole moment per unit volume dipoles per unit volume

목원대학교 전자정보통신공학부 전자기학 5-10 The net increase in the bound charge within the closed surface The net total charge which crosses the elemental surface (*Resemblance to Gauss ’ s law)

목원대학교 전자정보통신공학부 전자기학 5-11 Generalize the definition of electric flux density Isotropic material: linear relationship between E and P

목원대학교 전자정보통신공학부 전자기학 Boundary Conditions for Perfect Dielectric Materials

목원대학교 전자정보통신공학부 전자기학 5-13

목원대학교 전자정보통신공학부 전자기학 5-14 The boundary conditions at the interface between a conductor and a dielectric How any charge introduced within a conductor arrives at the surface (surface charge)

목원대학교 전자정보통신공학부 전자기학 Capacitance Surface charge, normal electric field, equipotential surface The capacitance is a function only of the physical dimensions of the system of conductors and of the permittivity of the homogeneous dielectric.

목원대학교 전자정보통신공학부 전자기학 5-16 The total energy stored in the capacitor

목원대학교 전자정보통신공학부 전자기학 Several Capacitance Examples A coaxial capacitor (inner radius a, outer radius b) A spherical capacitor (inner radius a, outer radius b) Capacitance of an isolated spherical conductor

목원대학교 전자정보통신공학부 전자기학 5-18 Coating this sphere with a different dielectric material Multiple dielectrics

목원대학교 전자정보통신공학부 전자기학 Capacitance of a Two-Wire Line