p2020chap06 - PHYS-2020 General Physics II Course Lecture...

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PHYS-2020: General Physics II Course Lecture Notes Section VI Dr. Donald G. Luttermoser East Tennessee State University Edition 3.3
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Abstract These class notes are designed for use of the instructor and students of the course PHYS-2020: General Physics II taught by Dr. Donald Luttermoser at East Tennessee State University. These notes make reference to the College Physics, 9th Edition (2012) textbook by Serway and Vuille.
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VI. Induced Voltages and Inductance A. Magnetic Flux. 1. Michael Faraday demonstrated that electric currents can be pro- duced by a changing magnetic field = a changing B -field can produce an induced emf . 2. Consider a loop of wire in a uniform B -field. The magnetic flux in the loop is the sum of the B -field strength across the entire (cross-sectional) surface area of the loop: Φ B = vector B · vector A = B A = BA cos θ . (VI-1) B > Front view of loop Uniform B-field Loop of wire B > B > B > || θ Side view of loop VI–1
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VI–2 PHYS-2020: General Physics II a) Φ B is the magnetic flux measured in T · m 2 = Wb (weber). b) The value of the magnetic flux is proportional to the total number of lines passing through the loop. B. Faraday’s Law of Induction. 1. The emf induced in a circuit equals the rate of change of the magnetic flux through the circuit: E = - N ΔΦ B Δ t . (VI-2) a) E ≡ emf, N number of loops in the wire circuit, ΔΦ B / Δ t change in magnetic flux over time. b) Eq. (VI-2) is known as Faraday’s law of magnetic in- duction . c) The negative sign is included to indicate polarity of the induced emf. d) Faraday’s law, as it is written in Eq. (VI-2), represents the average induced emf. The instantaneous induced emf (using calculus), which describes the more precise version of Faraday’s law, would be given by E = - N lim Δ t 0 ΔΦ B Δ t = - N d Φ B dt . 2. The polarity mentioned in Faraday’s law can be found from Lenz’s law : a) Any induced electromotive force will be in the direction such that the magnetic flux it creates will oppose the change in the flux that produced it. b) More simply, the induced current tends to maintain the original flux through the circuit.
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Donald G. Luttermoser, ETSU VI–3 c) Lenz’s Law is one consequence of the principle of conser- vation of energy. We can see why through the following example: i) Move a permanent magnet towards the face of a closed loop of wire ( e.g. , a coil or solenoid). ii) An electric current is induced in the wire, because the electrons within it are subjected to an increas- ing magnetic field as the magnet approaches. iii) This produces an emf that acts upon them. The direction of the induced current depends on whether the north or south pole of the magnet is approach- ing: An approaching north pole will produce an anti- clockwise current (from the perspective of the magnet).
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