Physics 1161: Lecture 13
Generators & Motors
• Textbook Sections 23-6 – 23-9
http://www.walter-fendt.de/ph14e/electricmotor.htm
http://www.walter-fendt.de/ph14e/generator_e.htm
Review: Two uses of RHR’s
• Force on moving
charge in Magnetic
field
• Magnetic field produced by
moving charges
– Thumb: I (or v for + charges)
– Fingers: curl along B field
F
I
– Thumb: v (or I)
– Fingers: B
– Palm: F on + charge
+ + + +
Palm: out of page.
I
v
Review: Induction
• Lenz’s Law
– If the magnetic flux (B) through a loop changes, an
EMF will be created in the loop to oppose the change
in flux
– EMF
current (V=IR)
additional B-field.
• Flux decreasing => B-field in same direction as original
• Flux increasing => B-field in opposite direction of original
• Faraday’s Law
– Magnitude of induced EMF given by:
 

t

f  i
tf  ti
A conducting loop is halfway
into a magnetic field. Suppose
the magnetic field begins to
increase rapidly in strength.
Which of the following statements
is true?
1. The loop is pushed upward, toward the
20%
top of the page.
2. The loop is pushed downward, toward
the bottom of the page.
3. The loop is pulled to the left, into the
magnetic field.
4. The loop is pushed to the right, out of
the magnetic field.
5. The tension in the wires increases but
the loop does not move.
1
20%
20%
2
3
20%
4
20%
5
A conducting loop is halfway
into a magnetic field. Suppose
the magnetic field begins to
increase rapidly in strength.
Which of the following statements
is true?
1. The loop is pushed upward, toward the
20%
top of the page.
2. The loop is pushed downward, toward
the bottom of the page.
3. The loop is pulled to the left, into the
magnetic field.
4. The loop is pushed to the right, out of
the magnetic field.
5. The tension in the wires increases but
the loop does not move.
1
20%
20%
2
3
20%
4
20%
5
A current-carrying wire is pulled away
from a conducting loop in the direction
shown.
As the wire is moving, is there a cw current
33%
around the loop, a ccw current or no current?
33%
33%
1. There is a clockwise current around
the loop.
2. There is a counterclockwise current
around the loop.
3. There is no current around the loop.
1
2
3
A current-carrying wire is pulled away
from a conducting loop in the direction
shown.
As the wire is moving, is there a cw current
33%
around the loop, a ccw current or no current?
33%
33%
1. There is a clockwise current around
the loop.
2. There is a counterclockwise current
around the loop.
3. There is no current around the loop.
1
2
3
A square loop of copper
wire is pulled through a
region of magnetic field
as shown in the figure.
Rank in order, from strongest to weakest, the pulling
25%
25%
25% the
25%
forces,F1, F2, F3, and F4 that must be applied
to keep
loop moving at constant speed.
1. F2 = F4 > F1 = F3
2. F3 > F2 = F4 > F1
3. F3 > F4 > F2 > F1
4. F4 > F2 > F1 = F3
5. F4 > F3 > F2 > F1
1
2
3
4
A square loop of copper
wire is pulled through a
region of magnetic field
as shown in the figure.
Rank in order, from strongest to weakest, the pulling
25%
25%
25% the
25%
forces,F1, F2, F3, and F4 that must be applied
to keep
loop moving at constant speed.
1. F2 = F4 > F1 = F3
2. F3 > F2 = F4 > F1
3. F3 > F4 > F2 > F1
4. F4 > F2 > F1 = F3
5. F4 > F3 > F2 > F1
1
2
3
4
Motional emf
The lightbulb in the circuit has a
resistance of 12 Ω and consumes 5.0 W
of power; the rod is 1.25 m long and
moves to the left with a constant speed
of 3.1 m/s. What is the strength of the
magnetic field?
 mf 

t
t

B  l  x
2
I 
B lv  IR
Now …
IR
lv

 m f  B lv
t
P  IV  I R
To find I:
B 

B  A
(0.645 A )  (12  )
(1.25 m )  (3.1 m / s )
P
R

 2.00 T
and
5 .0 W
12 
 m f  IR
 0.645 A
Motional emf
The lightbulb in the circuit has a
resistance of 12 Ω and consumes 5.0 W
of power; the rod is 1.25 m long and
moves to the left with a constant speed
of 3.1 m/s. What external force is
required to maintain the rod’s constant
speed?
P 
F d
t
 F v
F 
P
v

5.0 W
3.1 m s
 1.61 N
Review: Rotation Variables
v, , f, T
• Velocity (v):
– How fast a point moves.
– Units: usually m/s

r
• Angular Frequency ():
– How fast something rotates.
– Units: radians / sec
v
v
v= r
• Frequency ( f ):
– How fast something rotates.
– Units: rotations / sec = Hz
f =  / 2
• Period (T):
– How much time one full rotation takes.
– Units: usually seconds
T=1/f=
2 / 
Generators and EMF
EMF is voltage!
side 1 = v B L sin(q)
1
•
v = r
side 1 = r B L sin(q)
side 2 = r B L sin(q)
loop = side 1 + side 2
 2r B L sin(q)
2rL = A
loop =  A B sin(q)
loop =  A B sin(t)

v
2 x
AB
q
v
r

t
AB
At which time does the loop have the
greatest emf (greatest / t)?
1. 1
2. 2
3. 3
0%
1
0%
2
0%
3
At which time does the loop have the
greatest emf (greatest / t)?
1. 1
2. 2
3. 3
1) Has greatest flux, but q = 0 so  = 0.
2) (Preflight example) q  30 so   AB/2.
3) Flux is zero, but q = 90 so  = AB.
0%
1
0%
2
0%
3
Comparison:
Flux vs. EMF
Flux is maximum
– Most lines thru loop
EMF is minimum
– Just before: lines enter from left
– Just after: lines enter from left
– No change!
Flux is minimum
– Zero lines thru loop
EMF is maximum
– Just before: lines enter from top.
– Just after: lines enter from bottom.
– Big change!
Checkpoint
Rotating Loop
Flux is _________ at moment shown.
Increasing
decreasing
not changing
When q=30°, the EMF
around the loop is:
increasing
decreasing
not changing
Which of the following graphs is the correct
graph of EMF vs. angle for the loop shown
above?
Checkpoint
Rotating Loop
Flux is decreasing at moment shown.
When q=30°, the EMF around the loop is:
increasing
q  30
EMF is increasing!
decreasing
not changing

q
Generator
Generators and Torque
 =  A B sin(q)
Voltage!
Connect loop to resistance R use I=V/R:
I =  A B sin(q) / R
Recall:
t = A B I sin(q)
=  A2 B2 sin2(q)/R
•

v
x
r
Torque, due to current and B field, tries to slow
spinning loop down. Must supply external torque to keep it spinning at
constant 
q
v
Generator
A generator consists of a square coil of wire with 40 turns, each side is 0.2 meters long, and
it is spinning with angular velocity  = 2.5 radians/second in a uniform magnetic field
B=0.15 T. Determine the direction of the induced current at instant shown. Calculate the
maximum emf and torque if the resistive load is 4.
 = NA B  sin(q)
Units?

v
v
t = NI A B sin(q)
Units?
•
x
Generator
A generator consists of a square coil of wire with 40 turns, each side is 0.2 meters long, and
it is spinning with angular velocity  = 2.5 radians/second in a uniform magnetic field
B=0.15 T. Determine the direction of the induced current at instant shown. Calculate the
maximum emf and torque if the resistive load is 4.
 = NA B  sin(q)

= (40) (0.2m)2 (0.15T) (2.5 radians/s)
v
v
= 0.6 Volts
q
x
t = NI A B sin(q)
I m ax 
em f m ax
R
•

0.6V
4
 0.15 A
t = 40*I0.15A*(0.2m)2 * 0.15 T* 1
= 0.036 Newton-meters
Note: Emf is maximum at
q=90
Note: Torque is maximum at
q=90
Power Lines
Checkpoint
• Power is transferred from the power plant to your
house through high voltage power lines because:
• Generators at power plants operate at high voltages.
• It will decrease power loss.
• The power company wants to discourage people
from climbing on the lines.
Motor
An electric motor is exactly the opposite of a
generator – it uses the torque on a current loop to
create mechanical energy.