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Chapter 23

Chapter 23. Faraday’s Law and Induction. 23.1 Michael Faraday. 1791 – 1867 British experimental physicist Contributions to early electricity include Invention of motor, generator, and transformer Electromagnetic induction Laws of electrolysis. Induction.

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Chapter 23

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  1. Chapter 23 Faraday’s Law and Induction

  2. 23.1 Michael Faraday • 1791 – 1867 • British experimental physicist • Contributions to early electricity include • Invention of motor, generator, and transformer • Electromagnetic induction • Laws of electrolysis

  3. Induction • A changing magnetic field produces an induced current on a circuit without the present of a battery in the circuit • There is an induced emf associated with the induced current • Faraday’s Law of Induction describes the induced emf

  4. EMF Produced by a Changing Magnetic Field, • When the magnet is held stationary, there is no deflection of the ammeter • Therefore, there is no induced current • Even though the magnet is inside the loop

  5. EMF Produced by a Changing Magnetic Field, • A loop of wire is connected to a sensitive ammeter • When a magnet is moved toward the loop, the ammeter deflects • The deflection indicates a current induced in the wire

  6. EMF Produced by a Changing Magnetic Field, • The magnet is moved away from the loop • The ammeter deflects in the opposite direction

  7. EMF Produced by a Changing Magnetic Field, Summary • The ammeter deflects when the magnet is moving toward or away from the loop • The ammeter also deflects when the loop is moved toward or away from the magnet • An electric current is set up in the coil as long as relative motion occurs between the magnet and the coil • This is the induced current that is produced by an induced emf

  8. Faraday’s Experiment – Set Up • A primary coil is connected to a switch and a battery • The wire is wrapped around an iron ring • A secondary coil is also wrapped around the iron ring • There is no battery present in the secondary coil • The secondary coil is not electrically connected to the primary coil

  9. Faraday’s Experiment – Findings • At the instant the switch is closed, the galvanometer (ammeter) needle deflects in one direction and then returns to zero • When the switch is opened, the galvanometer needle deflects in the opposite direction and then returns to zero • The galvanometer reads zero when there is a steady current or when there is no current in the primary circuit

  10. Faraday’s Experiment – Conclusions • An electric current can be produced by a time-varying magnetic field • This would be the current in the secondary circuit of this experimental set-up • The induced current exists only for a short time while the magnetic field is changing • This is generally expressed as: an induced emf is produced in the secondary circuit by the changing magnetic field • The actual existence of the magnetic field is not sufficient to produce the induced emf, the field must be changing

  11. Magnetic Flux • To express Faraday’s finding mathematically, the magnetic flux is used • The flux depends on the magnetic field and the area:

  12. Faraday’s Law – Statements • Faraday’s Law of Induction states that the emf induced in a circuit is equal to the time rate of change of the magnetic flux through the circuit • Mathematically,

  13. Faraday’s Law – Example • Assume a loop enclosing an area A lies in a uniform magnetic field • The magnetic flux through the loop is FB = B A cos q • The induced emf is

  14. Ways of Inducing an emf • The magnitude of the field can change with time • The area enclosed by the loop can change with time • The angle q between the field and the normal to the loop can change with time • Any combination of the above can occur

  15. Applications of Faraday’s Law – Pickup Coil • The pickup coil of an electric guitar uses Faraday’s Law • The coil is placed near the vibrating string and causes a portion of the string to become magnetized • When the string vibrates at the some frequency, the magnetized segment produces a changing flux through the coil • The induced emf is fed to an amplifier

  16. 23.2 Motional emf • A motional emf is one induced in a conductor moving through a magnetic field • The electrons in the conductor experience a force that is directed along l

  17. Motional emf, cont • Under the influence of the force, the electrons move to the lower end of the conductor and accumulate there • As a result of the charge separation, an electric field is produced inside the conductor and gives rise to an electric force on the electrons • The charges accumulate at both ends of the conductor until the electric and magnetic forces are balanced

  18. Motional emf, final • For balance, q E = q v B or E = v B • A potential difference DV=vBl between the two ends of the conductor is maintained as long as the conductor continues to move through the uniform magnetic field • If the direction of the motion is reversed, the polarity of the potential difference is also reversed

  19. Sliding Conducting Bar • A bar moving through a uniform field and the equivalent circuit diagram • Assume the bar has zero resistance • The work done by the applied force appears as internal energy in the resistor R

  20. Sliding Conducting Bar, cont • The induced emf is • Since the resistance in the circuit is R, the current is

  21. Sliding Conducting Bar, Energy Considerations • The applied force does work on the conducting bar • This moves the charges through a magnetic field • The change in energy of the system during some time interval must be equal to the transfer of energy into the system by work • The power input is equal to the rate at which energy is delivered to the resistor

  22. AC Generators • Electric generators take in energy by work and transfer it out by electrical transmission • The AC generator consists of a loop of wire rotated by some external means in a magnetic field

  23. Induced emf In an AC Generator • The induced emf in the loops is • This is sinusoidal, with emax = N A B w

  24. 23.3 Lenz’ Law • Faraday’s Law indicates the induced emf and the change in flux have opposite algebraic signs • This has a physical interpretation that has come to be known as Lenz’ Law • It was developed by a German physicist, Heinrich Lenz

  25. Lenz’ Law, cont • Lenz’ Law states the polarity of the induced emf in a loop is such that it produces a current whose magnetic field opposes the change in magnetic flux through the loop • The induced current tends to keep the original magnetic flux through the circuit from changing

  26. Lenz’ Law – Example 1 • When the magnet is moved toward the stationary loop, a current is induced as shown in a • This induced current produces its own magnetic field that is directed as shown in b to counteract the increasing external flux

  27. Lenz’ Law – Example 2 • When the magnet is moved away the stationary loop, a current is induced as shown in c • This induced current produces its own magnetic field that is directed as shown in d to counteract the decreasing external flux

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