FWLec16 - A. F. Peterson: Notes on Electromagnetic Fields &...

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A. F. Peterson: Notes on Electromagnetic Fields & Waves 11/04 Fields & Waves Note #16 Faraday’s Law Objectives: Present Faraday’s Law in integral form and use it for several applications to illustrate the conversion of energy from mechanical into electrical form. Also introduce Faraday’s Law in differential form and consider some of its implications. Michael Faraday Previous Notes in this series have considered the various laws of electrostatics and magnetostatics. The force fields associated with electric charges and permanent magnetism were observed in ancient times, and equations describing the phenomena were known by about the year 1800. In the early 1800’s, many scientists tried to find a connection between the electric and magnetic effects. One such scientist, Michael Faraday, studied the problem for more than 10 years. Faraday became quite familiar with electrical phenomena, and during his years of research made a number of useful contributions, including the following: 1821 Faraday demonstrated a simple electric motor 1831 Faraday demonstrated a DC generator 1837 Faraday developed the polarization model for dielectric materials 1851 Faraday developed the commutator for DC motors In 1831, Faraday made the discovery that many others sought: he observed that moving a magnet through a closed loop of wire caused current to flow in that wire, resulting in a measurable voltage. This effect was induced by a change in the magnetic flux. Faraday had shown that electric and magnetic effects were linked, but only when the fields were changing as a function of time! Much research directed to finding a link between static electric and static magnetic effects found no link, and in fact today we recognize that static electric and static magnetic effects are independent of each other. It is time-varying electric and magnetic fields that are linked. Faraday’s Law To honor Faraday’s contribution, the following law is named after him. Faraday’s Law states that emf = =- ÚÚ Ú Ed d dt Bd S S C l (16.1)
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A. F. Peterson: Notes on Electromagnetic Fields & Waves 11/04 where S is an open surface that terminates on a closed contour C , and the right-hand screw convention (Note #13) is used to link the direction of dS with the orientation of C . The abbreviation “emf” was originally used to denote “electro-motive force,” a misnomer since the quantity is not a force but is rather a generalization of the notion of voltage. Observe that if the fields are not varying with time, (16.1) reduces to the previous constraint, that the circulation of the static electric field is always zero. Faraday’s law is often used to link physical motion within a system to an electrical response, and can also be used to explain the conversion of energy from one form (electrical or mechanical) to the other. We illustrate its utility by considering several examples.
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This note was uploaded on 01/27/2011 for the course ECE 3025 taught by Professor Citrin during the Spring '08 term at Georgia Institute of Technology.

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FWLec16 - A. F. Peterson: Notes on Electromagnetic Fields &...

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