1. Faraday’s Law and Induction
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

20. 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

21. 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

22. 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

23. 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

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

25. 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

36. 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

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

38. 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

39. 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

40. 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

41. 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

42. Figure 23.16: (a) As the conducting bar slides on the two fixed conducting rails, the flux due to the magnetic field directed inward through the area enclosed by the loop increases in time. By Lenz’s law, the induced current must be counterclockwise so as to produce a counteracting magnetic field directed outward from the page. (b) When the bar moves to the left, the induced current must be clockwise. Why?