University:
California State University, Northridge
Course:
PHYS 100B | General Physics II
Academic year:

2013
Views:

298

Pages:

19
Author:

Felicity Fischer

Chapter 23 Magnetic Flux and Faraday’s Law of induction Outline 23-1 Induced Electromotive Force 23-2 23-3 Magnetic Flux Faraday’s Law of Induction 23-4 Lens’s Law 23-5 Mechanical Work 23-6 Generators and Motors 23-10 Transformers 23-3 Faraday’s Law of Induction The induced emf (voltage) is proportional to the rate of the magnetic flux change with the time: Faraday’s Lay of Induction  final   initial    N  N T final  Tinitial t SI unit: V Where, N is the number of turns in the loop. (23  3) Magnitude of the Induce EMF   N t SI unit: V N  final   initial T final  Tinitial (23  4) Problem 23-15 The area of a 120-turn coil / loop oriented its plane perpendicular to a 0.20-T magnetic field is 0.050 m2. Find the average induced emf in this coil, if the magnetic field reverses its direction in 0.34 s. Solution: The magnetic flux is changed from BA to –BA. According to (23-4),  BA    BA  2 BA  N N N t t t  120 2  0.20 T   0.050 m 2  0.34 s  7.1 V Example 23-2 Bar Magnetic Induction A bar magnet is moved rapidly toward a 40-turn circular coil of wire. As the magnet moves, the average value of Bcos over the area of the coil increase from 0.0125T to 0.45 T in 0.250 s. If the radius of the coils is 3.05 cm, and the resistance of its wire is 3.55 , find the magnet of (a) the induced emf and (b) the induced current.   N t N  final   initial T final  Tinitial Example 23-2 Bar Magnet Induction Solution A 1). The magnetic Flux through the loop,  i   Bi cos( ) A  (0.0125T ) (0.0305m) 2  3.65 10 5 T  m 2  f   B f cos  A  (0.450T ) (0.0305m) 2  1.32 10 3 T  m 2 2) The induced emf, N  final   initial T final  Tinitial 1.32 10 3 T  m 2  3.65  10 5 T  m 2  (40) 0.250 s B 3) Using Ohm’s law to find the current, V 0.205V I   0.0577 A R 3.55  0.205 V 23-4 Lens’s Law Lens’s law can be used to explain the minus sign of Faraday’s law and determine the direction of the induced current in a circuit/loop. Lens’s Law An induced current always flows in a direction that opposes the change (of the magnetic flux) that causes it. Two Cases: The Force also against the moving! Figure 23-8 Applying Lenz’s Law to a Magnet Moving Toward ( a), and Away (b) From a Current Loop Another Example Figure 23-9 Lenz’s Law Applied to a Decreasing Magnetic Field Motional EMF A rod is falling down in a uniform B (because of gravity). Since the change of the magnetic flux in the loop, it creates a current. How to determine the direction of the current? Figure 23-10 Motional emf Lens’s Law is applied to determined the direction of the current ! Figure 23-11 Determining the Direction of an Induced Current Summary Faraday’s Lay of Induction  final   initial    N  N T final  Tinitial t (23  3) SI unit: V Lens’s Law An induced current always flows in a direction that opposes the change (of the magnetic field) that causes it. Exercise 23-1 The induced emf in a single loop of wire has a magnitude of 1.48V when the magnetic flux is changed from 0.850 Tm2 to 0.110 Tm2. How much time is required for this change flux? Solution Since   N t N  final   initial (23  4) T final  Tinitial We have T final  Tinitial  N  (1)  final   initial  0.110T  m 2  0.850T  m 2 1.48V  0.500 s