Physics 2112Unit 16
Concept:Motional EMF
Unit 16, Slide 1
The Plan
• Really odd formula coming:
Unit 16, Slide 2
dt
d B
• Spend a bit of time seeing that it makes sense (See prelecture for additional info.)
• Do two examples problem in detail.
• Move on to use formula.
X X X X X X X X
X X X X X X X X
X X X X X X X X
X X X X X X X X
X X X X X X X X
Motional EMF
BvqF
Motion of a conductor through B field can cause potential difference. (Remember Hall Effect clicker question?)
v
B
+ -F
F
+
-
+
-E
+
-E+
FB
FE
qEqvB
ELV L
vBE
Unit 16, Slide 3
vBV
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
Electricity & Magnetism Lecture 16, Slide 4
Which of the following statements is true? A. A motional emf exists in the bar
for case (a), but not for case (b) B. A motional emf exists in the bar
for case (b), but not for case (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 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.
CheckPoint 2A
Electricity & Magnetism Lecture 16, Slide 5
The motion of the green bar creates a current through the bar
A. going up B. going down
x x x x x x x x
x x x x x x x x
x x x x x x x x
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.
CheckPoint 2b
Electricity & Magnetism Lecture 16, Slide 6
The current through this bar results in a force on the bar A. down B. up C. right D. left E. into the screen F. out of the screen
x x x x x x x x
x x x x x x x x
x x x x x x x x
A 10cm conducting bar (green) rests on two frictionless wires connected by a resistor R = 50 . WThe entire apparatus is placed in a uniform magnetic field of 0.5 T pointing into the screen.
Example 16.1
Electricity & Magnetism Lecture 16, Slide 7
What is the current through the resistor?
What is the force required to keep the bar moving at this constant velocity?
The bar is pulled to the right by a force, F, at a velocity of 8m/sec.
x x x x x x x x
x x x x x x x x
x x x x x x x x
Checkpoint 2
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 of the field on the right side.
x x x x x x x x
x x x x x x x x
x x x x x x x x
Checkpoint 3
A conducting rectangular loop moves with velocity v towards an infinite straight wire carrying current as shown.
In what direction is the induced current in the loop?
A. clockwise B. counterclockwise C. There is no induced current in the loop
Generator: Changing Orientation
Electricity & Magnetism Lecture 16, Slide 10
On which legs of the loop is charge separated?
A) Top and Bottom legs only B) Front and Back legs onlyC) All legsD) None of the legs
Parallel to top and bottom legsPerpendicular to front and back legs
Bv
At what angle q is emf the largest?A) q = 0 B) q = 45o
C) q = 90o
D) emf is same at all anglesLargest for q = 0 (v perp to B)
L
w
)cos(cos)2(2222 tABBw
LBvLLq
FEL
= v
Generator: Changing Orientation
Bv
Electricity & Magnetism Lecture 16, Slide 11
A rectangular loop rotates in a region containing a constant magnetic field as shown.
Checkpoint 4
Electricity & Magnetism Lecture 16, Slide 12
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
Example 16.2 (Loop moving from wire)
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 at a velocity of 9 m/sec. The wire carries 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
Electricity & Magnetism Lecture 16, Slide 13
Note that the loop is moving with a constant velocity. Fnet = 0.
What are the magnetic forces on the four edges of the loop?
Net Force on the loop
Electricity & Magnetism Lecture 16, Slide 14
I v
x L
h
B into page
I
Something must be doing positive work on the loop to keep it moving at constant v.
Change Area of loop Change magnetic
field through loopChange
orientation of loop relative to BFaraday’s Law
Notice the minus sign!!!
Putting it Together
AB
dt
d
Electricity & Magnetism Lecture 16, Slide 15