1. Chapter 21
Magnetic Induction
and Chapter 22.9: Transformers

2. Magnetic Induction Faraday’s Law Lenz’s Law
“A changing magnetic flux induces an electromotive force (emf)”
Lenz’s Law
“the magnetic field produced by an induced current always opposes any changes in the magnetic flux”

3. Example: Falling Magnet
Suppose a bar magnet falls downward through a loop of wire, north pole first.
What is the direction of the induced current?
Suppose a bar magnet falls upward through a loop of wire, south pole first. N v S v

4. Inductance Consider the circuit shown When the switch is closed
Current flows through the solenoid and produces a magnetic field
The magnetic field changes the flux through the solenoid
The changing flux induces an emf to oppose the change in flux

5. Inductance, cont.
Induced emf acts like a battery pushing current in the opposite direction
This phenomenon is called self-inductance (or inductance)
The current changing through a coil induces a current in the same coil
The induced current opposes the original applied current, from Lenz’s Law
Section 21.4

6. Inductance of a Solenoid
Faraday’s law can be used to find the inductance of a solenoid
L is the symbol for inductance
The unit of inductance is the henry
1 H = 1 V . s / A
The voltage across the solenoid can be expressed in terms of inductance
Section 21.4

7. Inductor The principle applies to all coils or loops of wire
The value of L depends on the physical size and shape of the circuit element
The circuit element that uses self-inductance is called an inductor
Section 21.4

8. Inductor, cont. The voltage drop across an inductor is
Whenever the current through an inductor changes, a voltage is induced in the inductor that opposes this change
Many inductors are constructed as small solenoids
Almost any coil or loop will act as an inductor
Section 21.4

9. Real Inductors
Most practical inductors are made by wrapping a wire coil around a magnetic material
The magnetic material increases the inductance
Magnetic material has greater permeability than free space
Most inductors contain a material that produces a larger L in a smaller package
Section 21.5

10. RL Circuit Combined with capacitors, they form RLC Circuits
An RL Circuit is a circuit composed of any number of resistors, inductors, and voltage sources
Combined with capacitors, they form RLC Circuits
RLC circuits can describe almost any electronic circuit
RLC circuits are discussed in Chapter 22
Section 21.5

11. RL Circuit, cont. Before switch is closed,
No current flows (open circuit) so
I = 0
No current suggests no potential difference across circuit components
VR = 0
VL = 0
Section 21.5

12. RL Circuit, cont. When switch is closed (t = 0),
Inductor keeps current at same value it was before so I = 0
No current in the resistor means no potential difference across the resistor
VR = 0
Kirchhoff’s loop rule indicates
VL = V
Section 21.5

13. RL Circuit, cont. After a long time (t = ∞),
Back emf from inductor decreases until there is no change in the current
VL = 0
Kirchhoff’s loop rule indicates
VR = V
All the voltage change is across the resistor
I = V / R
Section 21.5

14. RL Circuit, cont.
Because the inductor opposes any change in current, a similar phenomenon occurs when the switch is opened
Section 21.5

15. Time Constant for RL Circuit
The current at time t is found by
For a single resistor in series with a single inductor,
The voltage is given by VL = V e-t/τ
Section 21.5

16. Energy in an Inductor
Energy is stored in the magnetic field of an inductor
The energy stored in an inductor is
Very similar in form to the energy stored in the electric field of a capacitor
The expression for energy stored in a solenoid is
Section 21.6

17. Magnetic Energy Density
Energy contained in the magnetic field actually exists anywhere there is a magnetic field, not just in a solenoid
Can exist in “empty” space
The potential energy can also be expressed in terms of the energy density in the magnetic field
This expression is similar to the energy density contained in an electric field
Section 21.6

18. Induction Puzzle
Consider a very long solenoid is inserted at the center of a single loop of wire
The field from the solenoid at the outer loop is essentially zero
Resolution leads to electromagnetic waves (Chapter 23)
Section 21.8

19. Mutual Inductance
It is possible for the magnetic field of one coil to produce an induced current in a second coil
The coils are connected indirectly through the magnetic flux
The effect is called mutual inductance
Section 21.4

20. Transformers
Transformers make use of mutual inductance to increase or decrease the amplitude of an applied AC voltage
A simple transformer consists of two solenoid coils with the loops arranged so that all or most of the magnetic field lines and flux generated by one coil pass through the other coil
Section 22.9

21. Transformers, cont.
The wires are covered with a nonconducting layer so that current cannot flow directly from one coil to the other
An AC current in one coil will induce an AC voltage across the other coil
An AC voltage source is typically attached to one of the coils called the input coil
The other coil is called the output coil

22. Transformers, Equations
Faraday’s Law applies to both coils
If the input coil has Nin coils and the output coil has Nout turns, the flux in the coils is related by
The voltages are related by
Section 22.9

23. Transformers, final
The ratio of the turns can be greater than or less than one
Therefore, the input voltage can be transformed to a different value
Transformers cannot change DC voltages
Since they are based on Faraday’s Law
Section 22.9

24. Practical Transformers
Most practical transformers have central regions filled with a magnetic material
This produces a larger flux, resulting in a larger voltage at both the input and output coils
The ratio Vout / Vin is not affected by the presence of the magnetic material
Section 22.9

25. Transformers and Power
The output voltage of a transformer can be made much larger by arranging the number of coils
According to the principle of conservation of energy, the energy delivered through the input coil must either be stored in the transformer’s magnetic field or transferred to the output circuit
Over many cycles, the stored energy is constant
The power delivered to the input coil must equal the output power
Section 22.9

26. Power, cont. P = V I Pin = Pout only in an ideal transformer
if Vout > Vin, then Iout < Iin
Pin = Pout only in an ideal transformer
In real transformers, the coils always have a small electrical resistance which causes some power dissipation
For a real transformer, the output power is always less than the input power (usually by only a small amount)
Small current means little power loss to resistance of power lines
Section 22.9

27. Applications of Transformers
Transformers are used in the transmission of electric power over long distances
Power dissipation in a electrical wire is P = V I
DC voltage would waste too much energy in transmission
Transformers allow large AC voltage transmission with small current
Many household appliances use transformers to convert the AC voltage at a wall socket to the smaller DC voltages needed in many devices
Section 22.9

28. Applications of Induction
A ground fault interrupter (GFI) is a safety device used in many household circuits
It uses Faraday’s Law along with an electromechanical relay
The relay uses the current through a coil to exert a force on a magnetic metal bar in a switch
During normal operation, there is zero magnetic field in the relay
If the current in the return coil is smaller, a non-zero magnetic field opens the relay switch and the current turns off
Section 21.7

29. Electric Guitars
An electric guitar uses Faraday’s Law to sense the motion of the strings
The string passes near a pickup coil wound around a permanent magnet
As the string vibrates, it produces a changing magnetic flux
The resulting emf is sent to an amplifier and the signal can be played through speakers
Section 21.7

30. Railgun
Current produces a large magnetic field which interacts with the current to produce a large force on the projectile
Projectile speeds much greater than conventional ballistics are possible
Proposed uses are
Weapons
Space Program
Inertial Confinement Fusion