UNIT-2 EMF conductors and diodes PPT.pptx

EMF

1. UNIT-2 conductors and dielectrics

2. Syllabus Conductors and dielectrics in Static Electric Field, Current and current density- Continuity equation, Polarization-Boundary conditions, Method of images- Resistance of a conductor, Capacitance, Parallel plate, Coaxial and Spherical capacitors-Boundary conditions for perfect dielectric materials-Poisson’s equation, Laplace’s equation- Solution of Laplace equation- Application of Poisson’s and Laplace’s equations. 2 IFETCE\ECE\A.Devi\II yr\IV sem\EC 6403 EMF\Unit II\PPT\Ver1.3

3. Conductors and dielectrics in Static Electric Field Electrostatics - science related to the electric charges which are static i.e. are at rest. An electric charge has its effect in a region or a space around it. This region is called the electric field of that charge. An electric field produced due to stationary electric charge does not varies with time. 3 IFETCE\ECE\A.Devi\II yr\IV sem\EC 6403 EMF\Unit II\PPT\Ver1.3

4. Conductors and dielectrics in Static Electric Field It is time invariant & is called as static electric field. The study of such time invariant electric field in space or vacuum, produced by various types of static charge distributions is called electrostatics. 4 IFETCE\ECE\A.Devi\II yr\IV sem\EC 6403 EMF\Unit II\PPT\Ver1.3

5. APPLICATIONS Most of the computer peripheral devices like keyboards, liquid crystal displays work on the principle of electrostatics. A variety of machines such as X-ray machine & medical instruments used for electrocardiograms, scanning ,etc use the principle of electrostatics. Many industrial processes like spray painting, electro deposition, etc also uses the principle of electrostatics. 5 IFETCE\ECE\A.Devi\II yr\IV sem\EC 6403 EMF\Unit II\PPT\Ver1.3

6. APPLICATIONS COND… It is also used in the agricultural activities like sorting seeds, spraying to plants. Many components such as bipolar transistors, FET functions based on electrostatics. 6 IFETCE\ECE\A.Devi\II yr\IV sem\EC 6403 EMF\Unit II\PPT\Ver1.3

7. CONDUCTORS AND DIELECTRIC IN STATIC ELECTRIC FIELD A conductor is a material in which electrons are free to migrate over macroscopic distances within the material. Metals are good conductors because they have many free electrons per unit volume. Other materials with a smaller number of free electrons per unit volume are also conductors. Conductivity is a measure of the ability of the material to conduct electricity. 7 IFETCE\ECE\A.Devi\II yr\IV sem\EC 6403 EMF\Unit II\PPT\Ver1.3

8. CONDUCTORS AND DIELECTRIC IN STATIC ELECTRIC FIELD COND… The charges in the dielectrics are bound by the finite forces and hence called bound charges. As they are bound and not free, they cannot contribute the conduction process. But if the subjected to the electric field, they shift their relative positions, against the normal molecular and atomic forces. IFETCE\ECE\A.Devi\II yr\IV sem\EC 6403 EMF\Unit II\PPT\Ver1.3 8

9. Properties of Conductor Under static conditions, no charge and no electric field can exist at any point within the conducting material The charge can exist on the surface of the conductor giving rise to the surface charge density Within a conductor, charge density is always zero The conductivity of ideal conductor is infinite The conductor surface is an equipotential surface 9 IFETCE\ECE\A.Devi\II yr\IV sem\EC 6403 EMF\Unit II\PPT\Ver1.3

10. Properties of Dielectric The dielectrics does not contain free charges but contain bound charges. Bound charges are under the internal molecular and atomic forces and cannot contribute to the conduction. Due to the polarization, the dielectrics can store energy. Due to the polarization, the flux density of dielectric increases by amount equal to the polarization . 10 IFETCE\ECE\A.Devi\II yr\IV sem\EC 6403 EMF\Unit II\PPT\Ver1.3

11. Current Displacement Current: Displacement current is defined as the rate of change, at any point in space, of electric displacement in time varying field (or) the current flows through the capacitor. It is also known as Maxwell’s displacement Current. Displacement current density can be simply denoted as J D . 11 IFETCE\ECE\A.Devi\II yr\IV sem\EC 6403 EMF\Unit II\PPT\Ver1.3

12. Current Density Current density is defined as the current per unit area. The current density can also be defined as the current passing through the unit surface area, when the surface is held normal to the direction of the current. The current density is measured in A/m 2 . J= I/A Amp/square m 12 IFETCE\ECE\A.Devi\II yr\IV sem\EC 6403 EMF\Unit II\PPT\Ver1.3

13. Continuity Equation If the current flows outwards from the closed surface, then it is constituted due to the outward flow of positive charges from the closed surface S. The continuity equations tells that, there must be decrease of an equal amount of positive charge inside the closed surface. Hence the outward rate of flow of positive charge gets balanced by the rate of decrease of charge inside the closed surface. While the differential form of continuity equation states that the current, diverging from a small volume per unit volume is equal to the time rate of decrease of charge per unit volume at every point. 13 IFETCE\ECE\A.Devi\II yr\IV sem\EC 6403 EMF\Unit II\PPT\Ver1.3

14. Polarization The alignment of the dipole moments of the permanent or induced dipoles in the direction of applied electric field is called polarization or electric polarizations. The magnitude of the induced dipole moment p is directly proportional to the external electric field E. p = α E, Where α is the constant of proportionality and is called molecular polarizability . It can also be said as dipole moment/ unit volume. 14 IFETCE\ECE\A.Devi\II yr\IV sem\EC 6403 EMF\Unit II\PPT\Ver1.3

15. POLARIZATION IN DIELECTRICS The charges induced on the surface of the dielectric (insulator) reduce the electric field. 15 IFETCE\ECE\A.Devi\II yr\IV sem\EC 6403 EMF\Unit II\PPT\Ver1.3

16. POLARIZATION IN DIELECTRICS “ Polarization ” of a dielectric in an electric field E gives rise to thin layers of bound charges on the dielectric’s surfaces, creating surface charge densities + s i and – s i . 16 IFETCE\ECE\A.Devi\II yr\IV sem\EC 6403 EMF\Unit II\PPT\Ver1.3

17. “ POLARIZATION” OF A DIELECTRIC IN AN ELECTRIC FIELD (E) 17 IFETCE\ECE\A.Devi\II yr\IV sem\EC 6403 EMF\Unit II\PPT\Ver1.3

18. Boundary Condition Within a homogeneous medium, there are no abrupt changes in E or D . However, at the interface between two different media (having two different values of e), it is obvious that one or both of these must change abruptly. To derive the boundary conditions on the normal and tangential field conditions, we shall apply the integral form of the two fundamental laws to an infinitesimally small region that lies partially in one medium and partially in the other. 18 IFETCE\ECE\A.Devi\II yr\IV sem\EC 6403 EMF\Unit II\PPT\Ver1.3

19. Boundary Condition on Normal Component of D Consider an infinitesimal cylinder (pillbox) with cross-sectional area D s and height D h lying half in medium 1 and half in medium 2: D s D h/2 D h/2 x x x x x x 19 IFETCE\ECE\A.Devi\II yr\IV sem\EC 6403 EMF\Unit II\PPT\Ver1.3

20. Boundary Condition Applying Gauss’s law to the pillbox, we have 20 IFETCE\ECE\A.Devi\II yr\IV sem\EC 6403 EMF\Unit II\PPT\Ver1.3

21. Boundary Condition The boundary condition is If there is no surface charge For non-conducting materials, r s = 0 unless an impressed source is present. 21 IFETCE\ECE\A.Devi\II yr\IV sem\EC 6403 EMF\Unit II\PPT\Ver1.3

22. Boundary Condition on Tangential Component of E Consider an infinitesimal path abcd with width Dw and height Dh lying half in medium 1 and half in medium 2: D h/2 D h/2 D w a b c d 22 IFETCE\ECE\A.Devi\II yr\IV sem\EC 6403 EMF\Unit II\PPT\Ver1.3

23. Boundary Condition on Tangential Component of E a b c d 23 IFETCE\ECE\A.Devi\II yr\IV sem\EC 6403 EMF\Unit II\PPT\Ver1.3

24. Boundary Condition on Tangential Component of E The boundary condition is 24 IFETCE\ECE\A.Devi\II yr\IV sem\EC 6403 EMF\Unit II\PPT\Ver1.3

25. Electrostatic Boundary Conditions - Summary At any point on the boundary, the components of E 1 and E 2 tangential to the boundary are equal the components of D 1 and D 2 normal to the boundary are discontinuous by an amount equal to any surface charge existing at that point 25 IFETCE\ECE\A.Devi\II yr\IV sem\EC 6403 EMF\Unit II\PPT\Ver1.3

26. Methods of Images The replacement of the actual problem with boundaries by an enlarged region or with image charges but no boundaries is called the method of images. Method of images is used in solving problems of one or more point charges in the presence of boundary surfaces. 26 IFETCE\ECE\A.Devi\II yr\IV sem\EC 6403 EMF\Unit II\PPT\Ver1.3

27. Methods of Images Cond … Method of images is particularly useful for evaluating potential and field quantities due to charges in the presence of conductors without actually solving for Poisson’s (or Laplace’s) equation. Utilizing the fact that a conducting surface is an equipotential , charge configurations near perfect conducting plane can be replaced by the charge itself and its image so as to produce an equipotential in the place of the conducting plane. 27 IFETCE\ECE\A.Devi\II yr\IV sem\EC 6403 EMF\Unit II\PPT\Ver1.3

28. Resistance of a Conductor The ratio of potential difference between the two ends of the conductors to the current flowing through is the resistance of the conductor. For non-uniform fields, 28 IFETCE\ECE\A.Devi\II yr\IV sem\EC 6403 EMF\Unit II\PPT\Ver1.3

29. CAPACITANCE Current i c associated with the capacitance C is related to the voltage across the capacitor by Where dv c / dt is a measure of the change in v c in a vanishingly small period of time. The function dv c / dt is called the derivative of the voltage v c with respect to time t. 29 IFETCE\ECE\A.Devi\II yr\IV sem\EC 6403 EMF\Unit II\PPT\Ver1.3

30. CAPACITORS IN SERIES Capacitors, like resistors, can be placed in series and in parallel. When placed in series, the charge is the same on each capacitor. 30 IFETCE\ECE\A.Devi\II yr\IV sem\EC 6403 EMF\Unit II\PPT\Ver1.3

31. CAPACITORS IN PARALLEL Placing capacitors in parallel the voltage across each capacitor is the same. The total charge is the sum of that on each capacitor. 31 IFETCE\ECE\A.Devi\II yr\IV sem\EC 6403 EMF\Unit II\PPT\Ver1.3

32. ENERGY STORED BY A CAPACITOR The ideal capacitor does not dissipate any energy supplied to it. It stores the energy in the form of an electric field between the conducting surfaces. The power curve can be obtained by finding the product of the voltage and current at selected instants of time and connecting the points obtained. W C is the area under the curve. 32 IFETCE\ECE\A.Devi\II yr\IV sem\EC 6403 EMF\Unit II\PPT\Ver1.3

33. ENERGY STORED BY A CAPACITOR 33 IFETCE\ECE\A.Devi\II yr\IV sem\EC 6403 EMF\Unit II\PPT\Ver1.3

34. Parallel plate A parallel-plate capacitor consists of two conducting plates with equal and opposite charges. Here is the electric field: 34 IFETCE\ECE\A.Devi\II yr\IV sem\EC 6403 EMF\Unit II\PPT\Ver1.3

35. Parallel plate 35 IFETCE\ECE\A.Devi\II yr\IV sem\EC 6403 EMF\Unit II\PPT\Ver1.3

36. CAPACITORS AND DI-ELECTRICS 36 IFETCE\ECE\A.Devi\II yr\IV sem\EC 6403 EMF\Unit II\PPT\Ver1.3

37. Parallel plate For parallel plate capacitor: C = e o A/d 37 IFETCE\ECE\A.Devi\II yr\IV sem\EC 6403 EMF\Unit II\PPT\Ver1.3

38. Cylindrical C apacitor For cylindrical capacitor: C = 2 p e o (L/ ln [b/a]) 38 IFETCE\ECE\A.Devi\II yr\IV sem\EC 6403 EMF\Unit II\PPT\Ver1.3

39. S pherical C apacitor For spherical capacitor [inner radius a, out radius b, air (or vacuum) in between] C = 4 p e o (a b/[b-a]) For an isolated sphere of radius R, b → ∞ C = 4 p e o R 39 IFETCE\ECE\A.Devi\II yr\IV sem\EC 6403 EMF\Unit II\PPT\Ver1.3

40. POISSON’S AND LAPLACE EQUATIONS A useful approach to the calculation of electric potentials relates potential to the charge density. The electric field is related to the charge density by the divergence relationship The electric field is related to the electric potential by a gradient relationship, 40 IFETCE\ECE\A.Devi\II yr\IV sem\EC 6403 EMF\Unit II\PPT\Ver1.3

41. POISSON’S AND LAPLACE EQUATIONS Therefore the potential is related to the charge density by Poisson's equation In a charge-free region of space, this becomes Laplace's equation 41 IFETCE\ECE\A.Devi\II yr\IV sem\EC 6403 EMF\Unit II\PPT\Ver1.3

42. POISSON’S AND LAPLACE EQUATIONS IN DIFFERENT COORDINATE SYSTEMS 42 IFETCE\ECE\A.Devi\II yr\IV sem\EC 6403 EMF\Unit II\PPT\Ver1.3

43. Solution of Laplace Equation The Procedure to solve a problem involving laplace Equation: Solve the Laplace equation using method of integration. Assume constants of integration as per the requirement Determine the constants applying the boundary conditions given or known for the region. The solution obtained in above step with constant obtained in an unique solution. IFETCE\ECE\A.Devi\II yr\IV sem\EC 6403 EMF\Unit II\PPT\Ver1.3 43

44. Solution of Laplace Equation Then can be obtained for the potential field V obtained, using gradient operation - V. For homogeneous medium, can be obtained as At the surface,  s =D N , hence once is known, the normal component D N to the surface is known. Then the charge induced on the conductor surface can be obtained. Once the charge induced is known and potential V is known then the capacitance C can be obtained. IFETCE\ECE\A.Devi\II yr\IV sem\EC 6403 EMF\Unit II\PPT\Ver1.3 44

45. Application of Poisson’s and Laplace’s equations Used to solve the partial differential equations for unique solutions, Boundary conditions Coaxial capacitance with single and two dielectric Spherical capacitance with single and two dielectric IFETCE\ECE\A.Devi\II yr\IV sem\EC 6403 EMF\Unit II\PPT\Ver1.3 45