Electromagnetic Field Theory

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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 Email: [email protected].

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