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# Lec18_19_20-SteadyMagneticField - ECSE 351 Electromagnetic...

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ECSE 351 Electromagnetic Fields McGill University – ECE Dept. - Prof. Milica Popovi ć Lectures 17 & 18: The Steady Magnetic Field Objective: we want to be able to (in free-space…): Determine what are sources of magnetic field Observe how the magnetic field effects current distribution Note: When introducing the magnetic field for the first time, some facts will have to be taken “as is” with no lengthy derivations. Please be patient with these. If we decided to go in depth on how these conclusions were made, we would not have a chance to do anything else in the course, and it would be very difficult to find time to link what you are learning with real-life applications… and this is what we are ultimately trying to achieve.

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Sources of magnetic field: Sources of magnetic field: ¾ Permanent magnet ¾ Time-changing electric field ¾ DC current McGill – ECE – ECSE 351 Electromagnetic Fields – Prof. M. Popovic Chapter 8
Bio-Savart Law What does it define? - Magnetic field What is a source of this magnetic field? - A small differential DC element in free space (a “small piece of wire carrying current”): current I , length McGill – ECE – ECSE 351 Electromagnetic Fields – Prof. M. Popovic dL JJG

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Bio-Savart Law Magnetic field intensity McGill – ECE – ECSE 351 Electromagnetic Fields – Prof. M. Popovic H d JJJG
Bio-Savart Law 2 H 4R R IdL a d × = π JJG JJJG McGill – ECE – ECSE 351 Electromagnetic Fields – Prof. M. Popovic 2 H R I dL a × = π JJG JJG JG v Magnetic field intensity A/m

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Bio-Savart Law McGill – ECE – ECSE 351 Electromagnetic Fields – Prof. M. Popovic 2 H 4R R IdL a × = π JJG JJG JG v Jean-Baptiste Biot born April 21, 1774, Paris, France died Feb. 3, 1862, Paris In 1820 he and the physicist Félix Savart discovered that the intensity of the magnetic field set up by a current flowing through a wire is inversely proportional to the distance from the wire.
Bio-Savart Law 2 4R R I dL a H × = π JJG JJG JJG v 2 H R IdL a d × = π JJJG 2 vol R J ad v H × = π J GJ J G McGill – ECE – ECSE 351 Electromagnetic Fields – Prof. M. Popovic Magnetic field intensity A/m 2 S 4 R K S H R × = π JJ J G Current distribution: On a surface A/m

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