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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