Lecture 4

Electromagnetic Field Theory

“Our thoughts and feelings have Dr. G. V. Nagesh Kumar Professor and Head, Department of EEE, electromagnetic reality. JNTUA College of Engineering Pulivendula Manifest wisely.” Topics

1. Biot Savart’s Law 2. Ampere’s Law 3. Curl

2 Releation between Electric Field and Magnetic Field

On 21 April 1820, Ørsted published his discovery that a compass needle was deflected from magnetic north by a nearby electric current, confirming a direct relationship between electricity and magnetism.

3 Magnetic Field

4 Magnetic Field

5 Direction of Magnetic Field

6 Direction of Magnetic Field

7 Properties of Magnetic Field

8 Magnetic Field Intensity

• The quantitative measure of strongness or weakness of the magnetic field is given by magnetic field intensity or magnetic field strength. • It is denoted as H. It is a vector quantity • The magnetic field intensity at any point in the magnetic field is defined as the force experienced by a unit north pole of one Weber strength, when placed at that point. • The magnetic field intensity is measured in • Newtons/Weber (N/Wb) or • Amperes per metre (A/m) or • Ampere-turns / metre (AT/m). 9 Magnetic Field Density

10 Releation between B and H

11 Permeability

12 Biot Savart’s Law

13 Biot Savart’s Law

14 Biot Savart’s Law : Distributed Sources

15 Problem

16 Problem

17 H due to Infinitely Long Conductor

18 H due to Finite Long Conductor

19 H due to Finite Long Conductor

20 H at Centre of Circular Cylinder

21 H at Centre of Circular Cylinder

22 H on the axis of a Circular Loop

23 Ampere's Circuital Law

24 Ampere's Circuital Law

25 Ampere's Circuital Law : Applications

H due to Infinitely Long Conductor

26 Ampere's Circuital Law : Applications

H due to Coaxial Cable

27 Ampere's Circuital Law : Applications

H due to Coaxial Cable

28 Ampere's Circuital Law : Applications

H due to Coaxial Cable

29 Ampere's Circuital Law : Applications

H due to Coaxial Cable

30 Ampere's Circuital Law : Applications

H due to Coaxial Cable

31 Ampere's Circuital Law : Applications

H due to Infinite Sheet of Current

32 Ampere's Circuital Law : Applications

H due to Infinite Sheet of Current

33 Ampere's Circuital Law : Applications

H due to Infinite Sheet of Current

34 Ampere's Circuital Law : Applications

H due to Infinite Sheet of Current

35 Problem

36 Problem

37 Problem

38 Curl

• Curl gives the measure of angular velocity of a object. • If Curl is zero, it means the object is not rotating. • If Curl is not zero, its magnitude represents the speed of the object and its direction

39 Curl

40 Curl in three coordinate systems

41 Properties of Curl

42 Stokes Theoroem

43 Physical Meaning of Curl

44 Problem

45 Problem

46 Releation between Magnetic Flux and Density

47 Releation between Magnetic Flux and Density

48 Application of Magnetic Flux and Density Coaxial Cable

49 Problem

50 Problem

51 Problem

52 Problem

53 Magnetic Potential

54 Scalar Magnetic Potential

55 Laplace Equation for Scalar Magnetic Potential

56 Vector Magnetic Potential

57 Vector Magnetic Potential

58 A due to differential current elements

59 Problem

60 Problem

61 Problem

62 Problem

63 Problem

64 Problem : GATE 2013

65 Problem : GATE 2013

66 Problem

67 Solution

68 Solution

69 Solution

70 Problem

71 Solution

72 Solution

73 Problem

74 Problem

75 Problem

76 Problem

77 Problem

78 Maxwells Equations

79 Thank you

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