1. Conductors moving in B field
Physics 212
Lecture 16
Motional EMF
Induced emf !!
Conductors moving in B field

2. The Big Idea B
When a conductor moves through a region containg a magnetic field:
Magnetic forces may be exerted on the charge carriers in the conductor
X X X X X X X X X + - F L v
X X X X X X X X X + -
These forces produce a charge separation in the conductor + - E
This charge distribution creates an electric field in the conductor + - E FB FE
The equilibrium distribution is reached when the forces from the electric and magnetic fields cancel
The equilibrium electric field produces a potential difference (emf) in the conductor 05

3. Opposite forces on charges
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.
Checkpoint 1 B
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) A B C D
Rotate picture by 90o
(top view) v
X X X X X X X X X B X b a
Bar a
No force on charges
No charge separation
No E field
No emf + - F
Fb = qvB + -
Fa = 0
Bar b
Opposite forces on charges
Charge separation
E = vB
emf = EL = vBL
:22

4. Opposite forces on charges
A conducting bar (green) rests on two frictionless wires connected by a resistor as shown.
Checkpoint 2a V R I
Equivalent circuit
Changing Area A B
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 C D
Rotate picture by 90o A B v0
X X X X X X X X X B + - F
Fb = qv0B
Bar
Opposite forces on charges
Charge separation
E = v0B
emf = EL = v0BL
:22

5. Counterclockwise Current
A conducting bar (green) rests on two frictionless wires connected by a resistor as shown.
Checkpoint 2b
F points to left F I
Energy
External agent must exert force F to the right to maintain constant v0
This energy is dissipated in the resistor!
Changing Area A
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 B C D A B
Preflight 5 C D E
Counterclockwise Current
:22

6. 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 = 0
B = 5 T
Out of Screen v
Let’s step through this one
Checkpoint 5 20

7. - t + t - - + + - t + E L v Only leading side has charge separation
emf = BLv (cw current) v + - E L t + - E
Leading and trailing sides have charge separation
emf = BLv – BLv = 0 (no current) v L + - E t
Only trailing side has charge separation
emf = BLv (ccw current) 20

8. A wire loop travels to the right at a constant velocity
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 = 0
B = 5 T
Out of Screen v
Checkpoint 5 20

9. Changing B field Checkpoint 3 + - B  + - v I
A conducting rectangular loop moves with velocity v toward an infinite straight wire carrying current as shown.
Checkpoint 3
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 I  B v + - + - 20

10. Generator: Changing Orientation
On which legs of the loop is charge separated?
Top and Bottom legs only
Front and Back legs only
All legs
None of the legs
Perpendicular to front and back legs
parallel to top and bottom legs 22

11. Generator: Changing OrientationL w
At what angle q is emf the largest?
Largest for q = 0 (v perp to B)
(A) q = 0
(B) q = 45o
(C) q = 90o
(D) emf is same at all angles
= v 22

12. 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 B v  + - I X 20

13. Putting it together Faraday’s Law Change Area of loop
Change magnetic field through loop
Change orientation of loop relative to B
Faraday’s Law
We will study this law in detail next time !

14. Example Problem
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? v I h x L
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

15. Example Problem
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? v I h x L
What is the direction of the B field produced by the wire in the region of the loop?
Into the page
Out of the page
Left
Right Up

16. Example Problem B into page v I h x L
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?
B into page v I h x L
What is the emf induced on the left segment?
Top is positive
Top is negative
Zero

17. Example Problem B into page v I h x L perpendicular to wire
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?
B into page v I h x L
What is the emf induced on the top segment?
left is positive
left is negative
Zero
perpendicular to wire

18. Example Problem B into page v I h x L
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?
B into page v I h x L
What is the emf induced on the right segment?
top is positive
top is negative
Zero

19. Example Problem B into page v I h x L
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?
B into page v I h x L
Which expression represents the emf induced in the left wire
(A)
(B)
(C)

20. Example Problem B into page v I h x L
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?
B into page v I h x L
Which expression represents the emf induced in the right wire
(A)
(B)
(C)

21. Example Problem B into page v I h x L
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?
B into page v I h x L
Which expression represents the total emf in the loop?
(A)
(B)
(C)

22. Follow-Up eLeft > eRight B into page + - I Clockwise current v I 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.
B into page + -
eLeft > eRight I
Clockwise current v I h x L
What is the direction of the induced current?
(A)
Clockwise
(B)
Counterclockwise

23. Follow-Up B into page I v I 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.
B into page I v I h
What is the direction of the force exerted by the magnetic field on the loop? x L
(A) UP I
B into page
(B)
DOWN
Total force from B
Points to the left !!
(C)
LEFT
(B)
RIGHT
(B)
F = 0