Chapter 20
Induced Voltages and Inductance
1.
Induce emf and Magnetic flux
2.
Faraday’s law of induction
3.
Lenz’s law
4.
Motional emf
5.
Generators
6.
Self-Inductance
7.
RL circuits
8.
Energy stored in a magnetic field
1
Michael Faraday
1791 – 1867
Great experimental
scientist
Invented electric
motor, generator
and transformers
Discovered
electromagnetic
induction
Discovered laws of
electrolysis
2
Faraday’s Experiment –
Set Up
What is induced emf?
How is it produced?
3
Magnetic Flux
What is magnetic
flux?
How do I
calculate it?
What is the SI
units?
Why the angle
dependence?
Flux and B
4
Electromagnetic Induction –
An Experiment
What is electromagnetic
induction?
What is induced current?
5
Example
1.
The quarter-circle loop shown in figure has an area
of 15 cm2. A magnetic field, with B=0.16T exists in
the +x direction. Find the flux through the loop in
each orientation shown.
6
Faraday’s Law and
Electromagnetic Induction
What is Faraday’s law?
What is the formula?
What is the SI units?
How to change the flux?
What is Lenz’s law?
7
Example
1.
As shown a metal rod makes contact with a partial
circuit. The circuit is perpendicular to the magnetic
field. Find the induced emf if the rod moves with
velocity of v=2m/s. Assume L=0.5m
8
Lenz’ Law – Example
9
Example
1.
See figures
10
Example
1.
See figures
11
Applications of Faraday’s Law
– Ground Fault Interrupters
12
Applications of Faraday’s
Law – Apnea Monitor
13
Application of Faraday’s
Law – Motional emf
What is motional emf?
How is it produced?
The force on charges
The potential difference
14
Motional emf in a Circuit
How do I
calculate motional
emf?
Motional emf and
Battery
What is the
resulting current?
15
Example
1.
As shown, a metal rod makes contact with a
partial circuit and completes the circuit. The circuit
area is perpendicular to the magnetic field with
B=0.15T. If the resistance of the total circuit is 3
ohm, how large a force is needed to move the rod
as indicated with a speed of 2 m/s.
16
Lenz’ Law Revisited –
Moving Bar Example
How do I
calculate the
direction of
induced
current?
One possibility
17
Lenz’ Law, Bar Example
Another
possibility
Conservation of
energy
18
Lenz’ Law – Moving
Magnet Example
When applying Lenz’ Law, there are two
magnetic fields to consider
The external changing magnetic field that induces
the current in the loop
The magnetic field produced by the current in the
loop
19
AC Generators
What is a
generator?
How does it work?
Emf of the loop
20
DC Generators
21
Motors
What is a Motor?
Motors an Back
22
Joseph Henry
1797 – 1878
First director of the
Smithsonian
First president of the
Academy of Natural
Science
First to produce an electric
current with a magnetic
field
Improved the design of
the electro-magnetic and
constructed a motor
Discovered self-inductance
23
Self-inductance
What is self-inductance?
How do I calculate it?
What are it SI units?
What is inductance?
How do I calculate it?
24
Example
1.
A coiled telephone cord has 70 turns, a crosssectional diameter of 1.3 cm, and an unstrectched
length of 60 cm. Determine an approximate value
for the self-inductance of the unstretched cord.
25
Inductor and RL Circuit
What is an inductor?
How does it work in a
circuit?
RL circuit
What is the time
constant?
How do I find the current
in the circuit?
What is the energy
stored in the inductor?
26
Example
For the circuit shown, determine
1.
1.
2.
3.
4.
Time constant
Current after one time constant
Change in potential at t=0 and t=first time constant
The rate of change of current after first time constant
27