motional emf - university of illinoisphysics 212 lecture 3 music who is the artist? a) gram parsons...
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Physics 212 Lecture 16, Slide 1
Physics 212 Lecture 16
Motional EMF
Induced emf !! Conductors moving in B field
Physics 212 Lecture 3
Music Who is the Artist? A) Gram Parsons B) Tom Waits C) Elvis Costello D) Townes Van Zandt E) John Prine
Why?
Theme of the week? Guys who sing with Emmylou Harris !! I do like these albums.. Giving you a break from Jazz this week…
Physics 212 Lecture 16, Slide 5
f dl
Closed loop integral, so …
Ff
q
Electromotive Force (EMF): Force per
unit charge of ANY sort
e.g.:
Bf v B
Ef E
where
To get a non-zero EMF, need a force that can
push charges around a loop, i.e.
Units of EMF: work = force x distance EMF = force/q x distance = work/q =
Physics 212 Lecture 16, Slide 8
The Big Idea When a conductor moves through a region containg a magnetic field:
Magnetic forces may be exerted on the charge carriers in the conductor: Creates an -> potential difference across the ends of the bar:
05
v
X X X X X X X X X B
X X X X X X X X X
+ - F
F
BF qv B
L
due to ( )B BV f dl v L vBLB This is called MOTIONAL EMF:
Move a conductor in a magnetic field in the right way, and you’ve got a magnetic battery
in above example
Physics 212 Lecture 16, Slide 9
Putting it together
Change Area of loop Change magnetic field
through loop Change orientation of loop relative to B
Faraday’s Law
B A d
dt
We will study this law in detail & in another context next time !
Physics 212 Lecture 16, Slide 10
Rotate picture by 90o (top view)
v
X X X X X X X X X
B
X X X X X X X X X
X v
b a
:22
Bar a No magnetic force
on charges No charge separation
No emf
Checkpoint 1
A B C D
+ -
v || B Fa = 0
+ - F
F
Fb = qvB
Bar b Magnetic force on charges
Charge separation emf = (F/q)L = vBL
Two identical conducting bars (shown in end view) are moving through a vertical magnetic
field. Bar (a) is moving vertically and bar (b) is moving horizontally.
Which of the following is true?
A. A motional emf exists in the bar for case (a), but not (b)
B. A motional emf exists in the bar for case (b), but not (a)
C. A motional emf exists in the bar for both cases (a) and (b)
D. A motional emf exists in the bar for neither case (a) nor case (b)
B
Physics 212 Lecture 16, Slide 11 :22
Rotate picture by 90o
A B C D
Checkpoint 2a
A B
Changing Area
A conducting bar (green) rests on two frictionless wires connected by a resistor as shown.
The entire apparatus is placed in a uniform magnetic field pointing
into the screen, and the bar is given an initial velocity to the right.
The motion of the green bar creates a current through the bar
A. going up
B. going down
Physics 212 Lecture 16, Slide 12 :22
Rotate picture by 90o
A B C D
v0
X X X X X X X X X
B
X X X X X X X X X
+ - F
F
Fb = qv0B
Bar Opposite forces on charges
Charge separation emf = (F/q)L = v0BL
Checkpoint 2a
A B
V R
I
Equivalent circuit
Changing Area
A conducting bar (green) rests on two frictionless wires connected by a resistor as shown.
The entire apparatus is placed in a uniform magnetic field pointing
into the screen, and the bar is given an initial velocity to the right.
The motion of the green bar creates a current through the bar
A. going up
B. going down
Physics 212 Lecture 16, Slide 13 :22
A B C D
Preflight 5
Counterclockwise Current
I
BLIF
Energy External agent must exert force F to the right to maintain constant v0 This energy is dissipated in the resistor!
LBR
vBLF
RILBv
R
vBLFvP 2
Checkpoint 2b
Changing Area
F points to left
F
A B C D E
A conducting bar (green) rests on two frictionless wires connected by a resistor as shown.
The entire apparatus is placed in a uniform magnetic field pointing
into the screen, and the bar is given an initial velocity to the right.
The current through this bar results in a force on the bar
A. down
B. up
C. right
D. left
E. into the screen
Physics 212 Lecture 16, Slide 14 20
Checkpoint 5
A wire loop travels to the right at a constant velocity. Which plot best represents the induced
current in the loop as it travels from left of the region of magnetic field, through the magnetic
field, and then entirely out on the right side?
B = 5 T
Out of Screen
B = 0
v
Physics 212 Lecture 16, Slide 15 20
Checkpoint 5
Let’s step through this one
A wire loop travels to the right at a constant velocity. Which plot best represents the induced
current in the loop as it travels from left of the region of magnetic field, through the magnetic
field, and then entirely out on the right side?
B = 5 T
Out of Screen
B = 0
v
Physics 212 Lecture 16, Slide 16 20
v
Only leading side has charge separation emf = BLv (cw current)
L +
- fB
v +
- fB L
+
- fB
Leading and trailing sides have charge separation emf = BLv – BLv = 0 (no current)
Only trailing side has charge separation emf = BLv (ccw current)
t
t
t v L
+
- fB
A wire loop travels to the right at a constant velocity. Which plot best represents the induced current in
the loop as it travels from left of the region of magnetic field, through the magnetic field, and then entirely
out on the right side?
A wire loop travels to the right at a constant velocity. Which plot best represents the induced current in
the loop as it travels from left of the region of magnetic field, through the magnetic field, and then entirely
out on the right side?
A wire loop travels to the right at a constant velocity. Which plot best represents the induced current in
the loop as it travels from left of the region of magnetic field, through the magnetic field, and then entirely
out on the right side?
Physics 212 Lecture 16, Slide 17 20
Checkpoint 5
A wire loop travels to the right at a constant velocity. Which plot best represents the induced
current in the loop as it travels from left of the region of magnetic field, through the magnetic
field, and then entirely out on the right side?
B = 5 T
Out of Screen
B = 0
v
Physics 212 Lecture 16, Slide 18 20
Changing B field A conducting rectangular loop moves with velocity v toward an infinite straight wire carrying
current as shown.
What is the direction of the induced current in the loop?
A. clockwise
B. counter-clockwise
C. there is no induced current in the loop
Checkpoint 3
Physics 212 Lecture 16, Slide 19 20
I
B B
B B
v + -
+ -
Changing B field A conducting rectangular loop moves with velocity v toward an infinite straight wire carrying
current as shown.
What is the direction of the induced current in the loop?
A. clockwise
B. counter-clockwise
C. there is no induced current in the loop
Checkpoint 3
Physics 212 Lecture 16, Slide 20
Generator: Changing Orientation
22
On which legs of the loop is charge separated?
A) Top and Bottom legs only B) Front and Back legs only C) All legs D) None of the legs
Bv
parallel to top and bottom legs
Perpendicular to front and back legs
Physics 212 Lecture 16, Slide 21
Generator: Changing Orientation
22
At what angle q is emf the largest?
(A) q = 0 (B) q = 45o
(C) q = 90o
(D) emf is same at all angles
Bv
Largest for q = 0 (v perp to B)
L
w
)cos(cos)2
(2222 tABBw
LBvLLq
FEL q
= v
Physics 212 Lecture 16, Slide 22 20
Generator: Changing Orientation A rectangular loop rotates in a region containing a constant magnetic field as shown.
The side view of the loop is shown at a particular time during the rotation. At this time, what
is the direction of the induced (positive) current in segment ab?
A. from b to a
B. from a to b
C. there is no induced current in the loop at this time
Checkpoint 4
Physics 212 Lecture 16, Slide 23 20
Generator: Changing Orientation
B
v
v X
Bv
Bv
I + -
A rectangular loop rotates in a region containing a constant magnetic field as shown.
The side view of the loop is shown at a particular time during the rotation. At this time, what
is the direction of the induced (positive) current in segment ab?
A. from b to a
B. from a to b
C. there is no induced current in the loop at this time
Checkpoint 4
Physics 212 Lecture 16, Slide 24
Example Problem
I v
x L
h
A rectangular loop (h=0.3m L=1.2 m) with total resistance of 5W is moving away from a long straight wire carrying total current 8 amps. What is the induced current in the loop when it is a distance x=0.7 m from the wire?
•Conceptual Analysis:
•Long straight current creates magnetic field in region of the loop.
•Vertical sides develop emf due to motion through B field
•Net emf produces current
•Strategic Analysis:
•Calculate B field due to wire.
•Calculate motional emf for each segment
•Use net emf and Ohm’s law to get current
Physics 212 Lecture 16, Slide 25
Example Problem
I v
x L
h
A rectangular loop (h=0.3m L=1.2 m) with total resistance of 5W is moving away from a long straight wire carrying total current 8 amps. What is the induced current in the loop when it is a distance x=0.7 m from the wire?
What is the direction of the B field produced by the wire in the region of the loop?
A) Into the page
B) Out of the page
C) Left
D) Right
E) Up
Physics 212 Lecture 16, Slide 26
Example Problem
I v
x L
h
A rectangular loop (h=0.3m L=1.2 m) with total resistance of 5W is moving away from a long straight wire carrying total current 8 amps. What is the induced current in the loop when it is a distance x=0.7 m from the wire?
What is the emf induced on the left segment?
A) Top is positive
B) Top is negative
C) Zero
B into page
Bv
Physics 212 Lecture 16, Slide 27
Example Problem
I v
x L
h
A rectangular loop (h=0.3m L=1.2 m) with total resistance of 5W is moving away from a long straight wire carrying total current 8 amps. What is the induced current in the loop when it is a distance x=0.7 m from the wire?
What is the emf induced on the top segment?
A) left is positive
B) left is negative
C) Zero
B into page
Bv
perpendicular to wire
Physics 212 Lecture 16, Slide 28
Example Problem
I v
x L
h
A rectangular loop (h=0.3m L=1.2 m) with total resistance of 5W is moving away from a long straight wire carrying total current 8 amps. What is the induced current in the loop when it is a distance x=0.7 m from the wire?
What is the emf induced on the right segment?
A) top is positive
B) top is negative
C) Zero
B into page
Bv
Physics 212 Lecture 16, Slide 29
Example Problem
I v
x L
h
A rectangular loop (h=0.3m L=1.2 m) with total resistance of 5W is moving away from a long straight wire carrying total current 8 amps. What is the induced current in the loop when it is a distance x=0.7 m from the wire?
Which expression represents the emf induced in the left wire
B into page
(A)
(B)
(C)
Lvx
Ioleft
2
vBE qEqvB vBhEh
hvx
Ioleft
2
LvxL
Ioleft
)(2
x
IB o
2 hv
x
Io
2
Physics 212 Lecture 16, Slide 30
hvxL
Ioright
)(2
Example Problem
I v
x L
h
A rectangular loop (h=0.3m L=1.2 m) with total resistance of 5W is moving away from a long straight wire carrying total current 8 amps. What is the induced current in the loop when it is a distance x=0.7 m from the wire?
Which expression represents the emf induced in the right wire
B into page
(A)
(B)
(C)
hvx
Ioright
2
Lvxh
Ioright
)(2
vBE qEqvB vBhEh
hvxL
Io
)(2
)(2 xL
IB o
Physics 212 Lecture 16, Slide 31
hvxL
Ihv
x
I ooloop
)(22
Example Problem
I v
x L
h
A rectangular loop (h=0.3m L=1.2 m) with total resistance of 5W is moving away from a long straight wire carrying total current 8 amps. What is the induced current in the loop when it is a distance x=0.7 m from the wire?
Which expression represents the total emf in the loop?
B into page
(A)
(B)
(C)
hvxL
Ihv
x
I ooloop
)(22
0loop
RI
looploop
xLxhv
R
II oloop
11
2
Physics 212 Lecture 16, Slide 32
Follow-Up
I v
x L
h
A rectangular loop (h=0.3m L=1.2 m) with total resistance of 5W is moving away from a long straight wire carrying total current 8 amps.
What is the direction of the induced current?
B into page
(A)
(B)
Clockwise
Counterclockwise
+ +
- -
Left > Right
I
Clockwise current
Physics 212 Lecture 16, Slide 33
Follow-Up
I v
x L
h
A rectangular loop (h=0.3m L=1.2 m) with total resistance of 5W is moving away from a long straight wire carrying total current 8 amps.
What is the direction of the force exerted by the magnetic field on the loop?
B into page
(A)
(B)
UP
DOWN
I
(C) LEFT
(B) RIGHT
(B) F = 0
I
B into page
Total force from B Points to the left !!