Ch. 20 Part b
concept #1, 4, 5, 8, 10, 13,
Problem # 1, 3, 4, 5, 6, 9, 13, 15, 18,
19, 23, 25, 27, 35a, 39, 43, 47, 49
Lenz’s Law revisited
See pictures in book to practice getting the
direction of the induced current. page 671
Look to see what is the direction of the change of
flux.
The induced current will produce flux in the
opposite direction of the change in flux.
http://micro.magnet.fsu.edu/electromag/java/le
nzlaw/
Generators
• generators and motors operate on the
principle of electromagnetic induction
• generator converts mechanical energy to
electrical energy
• motor converts electrical energy to
mechanical
Electrical generator
Consists of a wire loop(s) rotated in a magnetic
field.
In a hydroelectric plant, falling water turns the
blades of a turbine to rotate the loop.
As the loop rotates, the magnetic flux through
the loop changes with time.
Changing flux induces an emf and a current.
= NBA sin t
the varies with time
N = number of turns
A = area or coil
B = field strength
= angular speed
Maximum emf from a generator
occurs when t = = 900 or 2700
= NBA
This occurs when the plane of the loop is
parallel to the magnetic field.
f where f is the frequency of rotation
In U.S. and Canada f = 60 Hz.
Motor is a generator acting in reverse.
Current is supplied to a loop by some outside
source.
The magnetic torque on a carrying current
loop, forces the loop to rotate.
Remember from Ch. 19 that the torque on a
current loop is: = B I A sin
Self Inductance
Consider a cicuit (current loop) with a switch, a
resistor, and a source of emf (battery).
When the switch is closed, the current does not
change from 0 to its maximum value of I = /R
immediately.
Faraday’s Law prevent this.
As the current increases from zero, a magnetic
field is produced and the flux through the loop
increases. The increasing flux induces an emf that
opposes the change in magnetic flux.
• The net voltage across the resistor is the emf
from the battery minus the induced emf.
• The opposing emf results in a gradual increase
in current.
• When the switch is closed, the current does
not immediately drop to zero either.
• This effect is called self-inductance
also see fig 20.25
Self Inductance
Faraday’s Law
= -N
B/
t
The change in flux comes from the change in
the current.
= - L I/ t
L = the inductance of the device
If the current is increasing, the induced emf is
negative.
Inductance
Inductance has units of henry (H)
1 H = 1 V s/A
These units can be found from the previous eqn.
By setting equal the equations:
= -N
and
B/ t
N
We can find: L N
B
I
B
I
= - L I/ t
Inductance of a solenoid
B
0
B
L
nI
BA
N
B
I
N
N
)I
0(
L
N
AI
0
L
N 2 AI
0
L
I
2
N
A
0
L
nL
2
L
V
(nL)
A
0
L
volume AL
2
n
AL
0
2
n
0 V
example 20.7
Calculate inductance of solenoid of 300 turns
-4m2.
and length 25 cm and area 4x10
2
4
2
300
(
4
x
10
m
)
7
2
L = 0N A/L = (4 10 Tm / A)
0.25 m
L = 0.181 mH
Calculate self induced emf in the solenoid if
the current decreases at rate of 50 A/s.
= -L I/ t = -0.181mH (-50 A/s)
=9.05 mV
(remember: H = V s/A)
RL circuits
Series circuit with a resistor and an inductor.
Resistor is used to limit the current flowing
through the circuit. Resistance has units of ohms
( ).
Inductor is a closely wrapped coil of many turns.
Has an inductance.
When current is turned on, it raises gradually to
the maximum value of I = V/R
V is the voltage provided by the battery.
Save this for next segment of class. Will be on
third exam.
Energy stored in a magnetic field
Inductors store energy in a magnetic field.
This is a potential energy.
PEL = ½ L I2
Note that this is similar to the expression for the
energy stored in a capacitor (PEC = ½ CV2)
example 20.9
12 V battery is hooked up to a 25
inductor.
resistor and a 5 H
Find the max current:
Imax = V/R = (12V)/(25 ) = 0.48 A
Find energy stored in the inductor when the current is maxed:
energy = ½ (5 H)(0.48A)2 = 0.576 J
Worry about part c for later.