Lect10Faraday - ECE 3030 Electromagnetic Fields and Waves...

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1 ECE 3030 Electromagnetic Fields and Waves Fall 2009 Lecture 10 2009/9/18 Electromagnetic Induction Faraday’s Law Revisited Non Uniqueness of Voltages in Magnetoquasistatics 1 Swartz and Rana 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 10: Instructor: Dr. Wesley E. Swartz Non-Uniqueness of Voltages in Magnetoquasistatics Field Energy Power – Energy Continuity + + - - 1 R 2 R I + _ () t I Inductance = L C t V λ Faraday’s Law Revisited Faraday’s Law : The line integral of the E-field around a closed contour is equal to negative of the time rate of change of the magnetic flux that goes through any arbitrary surface that is bounded by the closed contour. a d B t s d E =  A closed contour B 2 Swartz and Rana 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 10: Important Note : In electroquasistatics the line integral of E-field over a closed contour was always zero. In magnetoquasistatics this is NOT the case. a d H t o =  μ  = = 0 s d s d E φ Electromagnetic Induction Consider a closed contour through which the magnetic flux is changing with time: Since the line integral around the closed contour shown would not be zero, one can put a conductive wire in place of the contour and get current flowing through it because of the E field A closed contour s d E dt d a d B t s d E = =  3 Swartz and Rana 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 10: current flowing through it because of the E-field. Now suppose a current I is flowing through the wire: dt d R I R I R I R I s d E 2 1 2 1 = + + = + + - - 1 R 2 R I dt d R R I 2 1 1 + = The induced current in the wire produces its own magnetic field. Lenz’s Law is just an easy way to remember in which direction the induced current flows: Th l t t th t th i d d t ill fl i di ti h th t it Lenz’s Law Suppose an induced current I is flowing through the wire: dt d R R I 2 1 1 + = + + - - 1 R 2 R I 4 Swartz and Rana 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 10: The law states that the induced current will flow in a direction such that its own magnetic field opposes the time variation of the magnetic field that produced it. Example : Suppose the magnetic flux through the wire loop shown above was increasing with time (so that d l /d t > 0 ). Lenz’s Law tells us the induced current flows in the clockwise direction so that its own magnetic field opposes the increasing magnetic flux through the loop. In the equation above this fact comes from the negative sign on the right hand side. Non-Uniqueness of Voltages in Magnetoquasistatics (1) We know: Question : What is the voltage difference V 2 -V 1 ?
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This note was uploaded on 11/26/2009 for the course ECE 3030 at Cornell University (Engineering School).

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Lect10Faraday - ECE 3030 Electromagnetic Fields and Waves...

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