Chapter 23 Magnetic Flux and Faraday s Law of Induction

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1 Chapter 23 Magnetic Flux and Faraday s Law of Induction

2 Recall: right hand rule 2 10/28/2013

3 Units of Chapter 23 Induced Electromotive Force Magnetic Flux Faraday s Law of Induction Lenz s Law Mechanical Work and Electrical Energy Generators and Motors

4 Introduction Previous chapter: electric currents produce magnetic fields (Oersted s experiments) Is the opposite true: can magnetic fields create electric currents? (Faraday) 4 10/28/2013

Magnetic flux Just like in the case of electric flux, consider a situation where the magnetic field is uniform in magnitude and direction. Place a loop in the B-field.

5 Magnetic flux Just like in the case of electric flux, consider a situation where the magnetic field is uniform in magnitude and direction. Place a loop in the B-field. The flux, F, is defined as the product of the field magnitude by the area crossed by the field lines. Definition of Magnetic Flux F B A BAcos Units: T m 2 or Webers (Wb) The value of magnetic flux is proportional to the total number of magnetic field lines passing through 5 the loop. 10/28/2013

6 Problem 1: determining flux A square loop 2.00m on a side is placed in a magnetic field of strength 0.300T. If the field makes an angle of 50.0 with the normal to the plane of the loop, determine the magnetic flux through the loop. 6 10/28/2013

7 Induced EMF Faraday s experiment Picture Molecular Expressions Two circuits are not connected: no current? However, closing the switch we see that the compass needle moves and then goes back to its previous position Nothing happens when the current in the primary coil is steady But same thing happens when the switch is opened, except for the needle going in the opposite direction What is going on? 7 10/28/2013

8 Faraday s law of induction Induced current I v S N 8 10/28/2013

9 Faraday s law of induction I v B A current is set up in the circuit as long as there is relative motion between the magnet and the loop. I S N B I v 9 10/28/2013

10 Does there have to be motion? (induced) I I 10 10/28/ AC Delco 1 volt

11 Does there have to be motion? I 11 10/28/ AC Delco 1 volt

12 Does there have to be motion? (induced) I 12 10/28/ AC Delco 1 volt

13 NO!! Does there have to be motion? 13 10/28/ AC Delco 1 volt

14 Induced Electromotive Force Faraday s experiment: closing the switch in the primary circuit induces a current in the secondary circuit, but only while the current in the primary circuit is changing.

15 Induced Electromotive Force The current in the secondary circuit is zero as long as the current in the primary circuit is constant, and therefore the magnetic field in the iron bar is constant. Current flows in the secondary circuit while the current in the primary is changing. It flows in opposite directions depending on whether the magnetic field is increasing or decreasing. The magnitude of the induced current is proportional to the rate at which the magnetic field is changing.

16 Faraday s law of magnetic induction In all of those experiment induced EMF is caused by a change in the number of field lines through a loop. In other words, The instantaneous EMF induced in a circuit equals the rate of change of magnetic flux through the circuit. Lenz s law The number of loops matters 16 10/28/2013

17 Faraday s Law of Induction There are many devices that operate on the basis of Faraday s law. An electric guitar pickup:

18 Tape recorder: Faraday s Law of Induction

19 Applications: Ground fault interrupter SIDS monitor Metal detector 19 10/28/2013

20 Problem 2: EMF in a loop A wire loop of radius 0.30m lies so that an external magnetic field of strength +0.30T is perpendicular to the loop. The field changes to -0.20T in 1.5s. (The plus and minus signs here refer to opposite directions through the loop.) Find the magnitude of the average induced emf in the loop during this time. Find the induced current if the resistance of the wire is 3.55 Ω. B 20 10/28/2013

21 Recall: Faraday s Law of Induction Faraday s law: An emf is induced only when the magnetic flux through a loop changes with time.

22 Lenz s Law Lenz s Law An induced current always flows in a direction that opposes the change that caused it. Therefore, if the magnetic field is increasing, the magnetic field created by the induced current will be in the opposite direction; if decreasing, it will be in the same direction.

23 This conducting rod completes the circuit. As it falls, the magnetic flux decreases, and a current is induced. Lenz s Law

24 Lenz s Law The force due to the induced current is upward, slowing the fall. Since an emf is produced in the system, it is referred to as motional emf.

25 Mechanical Work and Electrical Energy This diagram shows the variables we need to calculate the induced emf.

26 Mechanical Work and Electrical Energy Change in flux: Induced emf: Electric field caused by the motion of the rod:

27 Motional EMF conducting rails We can apply Faraday's law to the complete loop. The change of flux through the loop is proportional to the change of area from the motion of the bar: F BA Bl x or (Faraday s law) current E I R F x E Bl Blv Blv t t R 27 10/28/2013 Motional EMF

28 Mechanical Work and Electrical Energy If the rod is to move at a constant speed, an external force must be exerted on it. This force should have equal magnitude and opposite direction to the magnetic force:

29 Mechanical Work and Electrical Energy The mechanical power delivered by the external force is: Compare this to the electrical power in the light bulb: Therefore, mechanical power has been converted directly into electrical power.

30 Summary of Chapter 23 A changing magnetic field can induce a current in a circuit. The magnitude of the induced current depends on the rate of change of the magnetic field. Magnetic flux: Faraday s law gives the induced emf:

31 Summary of Chapter 23 Lenz s law: an induced current flows in the direction that opposes the change that created the current. Motional emf: emf produced by a generator: An electric motor is basically a generator operated in reverse. Inductance occurs when a coil with a changing current induces an emf in itself.

General Physics (PHY 2140)

General Physics (PHY 2140) Lecture 15 Electricity and Magnetism Magnetism Applications of magnetic forces Induced voltages and induction Magnetic flux and induced emf Faraday s law http://www.physics.wayne.edu/~apetrov/phy2140/