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Physics 212 Lecture 13, Slide 3 06 Force on a wire carrying current I Cross sectional area A, Length L Number of charges/m 3 = n Each charge moving at V avg Force on each charge Total force on wire Use
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Physics 212 Lecture 13, Slide Physics 212 Lecture 13, Slide 11
Physics 212Physics 212Lecture 13Lecture 13
Forces and Torques on Currents
Physics 212 Lecture 13, Slide Physics 212 Lecture 13, Slide 22
Key Concepts:Key Concepts:
• Forces & Torques on loops of current Forces & Torques on loops of current due to a magnetic field.due to a magnetic field.
• The magnetic dipole moment.The magnetic dipole moment.
05
Physics 212 Lecture 13, Slide Physics 212 Lecture 13, Slide 3306
wireF I L B
Force on a wire carrying current I
Cross sectional area A, Length L
Number of charges/m3 = n
Each charge moving at Vavg
each avgF qv B
Force on each charge
wire each avgF N F Nqv x B
Total force on wire
avgqnAvInALN
Use
L
B
I
wireF
wireF I L B
L
Current- carrying wire in uniform B field
I
B
Out of page
Physics 212 Lecture 13, Slide Physics 212 Lecture 13, Slide 55
F IL B
ACT
ABC
08
Physics 212 Lecture 13, Slide Physics 212 Lecture 13, Slide 66
F IL B
ABC
ACT
10
Physics 212 Lecture 13, Slide Physics 212 Lecture 13, Slide 77
F IL B
What is the force on section d-a of the loop?What is the force on section d-a of the loop?A)A) ZeroZeroB)B) Out of the pageOut of the pageC)C) Into the pageInto the page
ACT
12
Physics 212 Lecture 13, Slide Physics 212 Lecture 13, Slide 88
Checkpoint 1a
13
ABC
“The net force on any closed loop is zero.”
Physics 212 Lecture 13, Slide Physics 212 Lecture 13, Slide 99
In which direction will the loop rotate?In which direction will the loop rotate? (assume the z axis is out of the page)(assume the z axis is out of the page)
A)A) Around the x axisAround the x axisB)B) Around the y axisAround the y axisC)C) Around the z axisAround the z axisD)D) It will not rotateIt will not rotate
x
y
15
Checkpoint 1b
Physics 212 Lecture 13, Slide Physics 212 Lecture 13, Slide 1010
R F
RF
Checkpoint 1c
17
ABCDE
y
Physics 212 Lecture 13, Slide Physics 212 Lecture 13, Slide 1111
Magnetic Dipole Moment
Area vectorMagnitude = AreaDirection uses right hand rule
Magnetic Dipole moment
turnsN IA
19
Physics 212 Lecture 13, Slide Physics 212 Lecture 13, Slide 1212
B
The torque always wants to lineThe torque always wants to line up with up with BB ! !
BB
B turnsturns toward toward BB
x
y
z
BB
B turnsturns toward toward BBx
y
z
21
Physics 212 Lecture 13, Slide Physics 212 Lecture 13, Slide 1313
B
B
In this caseIn this case is out of the page (using right hand rule)is out of the page (using right hand rule)
I
BB
B
x
y
z
is up (turnsis up (turns toward B)toward B)
22
Practice with and
Physics 212 Lecture 13, Slide Physics 212 Lecture 13, Slide 1414
B
Biggest when B
24
Checkpoint 2aThree different orientations of a magnetic dipole moment in a constant magnetic field are shown below. Which orientation results in the largest magnetic torque on the dipole?
Physics 212 Lecture 13, Slide Physics 212 Lecture 13, Slide 1515
Potential energy of a magnetic dipole moment
2 2
2
1
1 1
2 1 sin cosBU U d B d B
27
U B
B
1
B
2Rotate from 1 to 2
2 1 2 1 2 1cos cosU U B B B B
Lowest U parallel to B
Highest U antiparallel to B
-1.5
-1
-0.5
0
0.5
1
1.5
0 30 60 90 120 150 180
B
U
U = 0
Physics 212 Lecture 13, Slide Physics 212 Lecture 13, Slide 1717
U B
Checkpoint 2b
30
U = 0 U = -Bcos
U = +Bcos
Three different orientations of a magnetic dipole moment in a constant magnetic field are shown below. Which orientation has the most potential energy?
Physics 212 Lecture 13, Slide Physics 212 Lecture 13, Slide 1818
ACT
30
c
a
a
Three different orientations of a magnetic dipole moment in a constant magnetic field are shown below. We want to rotate the dipole in the CCW direction.
B
First, consider rotating to position c. What are the signs of the work done by you and the work done by the field?
A)Wyou > 0, Wfield > 0B)Wyou > 0, Wfield < 0C)Wyou < 0, Wfield > 0D)Wyou < 0, Wfield < 0
• U > 0, so Wfield < 0. Wyou must be opposite Wfield
• Also, torque and displacement in opposite directions Wfield < 0
fieldW U
Physics 212 Lecture 13, Slide Physics 212 Lecture 13, Slide 1919
ACT
30
c
a
a
Consider rotating the dipole to each of the three final orientations shown.
B
Does the sign of the work done by you depend on which position (a, b, or c) the dipole is rotated to?
A)YesB)NoThe lowest potential energy state is with dipole parallel to B. The potential energy will be higher at any of a, b, or c.
U B
Physics 212 Lecture 13, Slide Physics 212 Lecture 13, Slide 2020
CalculationCalculationA square loop of side a lies in the x-z plane with current I as shown. The loop can rotate about x axis without friction. A uniform field B points along the +z axis. Assume a, I, and B are known.
How much does the potential energy of the system change as the coil moves from its initial position to its final position. • Conceptual Analysis
– A current loop may experience a torque in a constant magnetic field• = X B
– We can associate a potential energy with the orientation of loop• U = - ∙ B
z
x
y
B .30˚
y
z
Iinitial final
• Strategic Analysis– Find – Calculate the change in potential energy from initial to final
a
B
32
Physics 212 Lecture 13, Slide Physics 212 Lecture 13, Slide 2121
CalculationCalculation
• What is the direction of the magnetic moment of this current loop in its initial position?
(A) (A) +x (B) (B) -x (C) (C) +y (D) (D) -yz
x ●●y
A square loop of side a lies in the x-z plane with current I as shown. The loop can rotate about x axis without friction. A uniform field B points along the +z axis. Assume a, I, and B are known.
z
x
y
B .30˚
y
z
Iinitial final
a
B
IA
z
y
.
X
Right Hand Rule34
Physics 212 Lecture 13, Slide Physics 212 Lecture 13, Slide 2222
CalculationCalculation
• What is the direction of the torque on the current loop in the initial position?
(A) (A) +x (B) (B) -x (C) (C) +y (D) (D) -y
A square loop of side a lies in the x-z plane with current I as shown. The loop can rotate about x axis without friction. A uniform field B points along the +z axis. Assume a, I, and B are known.
z
x
y
B .30˚
y
z
Iinitial final
a
B
Bz
y
.
X
36
Physics 212 Lecture 13, Slide Physics 212 Lecture 13, Slide 2323
CalculationCalculation
U B
• What is the potential energy of the initial state? (A) (A) Uinitial < 0 < 0 (B) (B) Uinitial = 0 = 0 (C) (C) Uinitial > 0 > 0
090
A square loop of side a lies in the x-z plane with current I as shown. The loop can rotate about x axis without friction. A uniform field B points along the +z axis. Assume a, I, and B are known.
z
x
y
B .30˚
y
z
Iinitial final
a
B
z
y
B
38
0 B
Physics 212 Lecture 13, Slide Physics 212 Lecture 13, Slide 2424
CalculationCalculation
• What is the sign of the potential energy in the final state? (A) (A) Ufinal < 0 < 0 (B) (B) Ufinal = 0 = 0 (C) (C) Ufinal > 0 > 0
A square loop of side a lies in the x-z plane with current I as shown. The loop can rotate about x axis without friction. A uniform field B points along the +z axis. Assume a, I, and B are known.
z
x
y
B .30˚
y
z
Iinitial final
a
B
initial final z
y
B
z
y
B
U B
40
0120
U B
0 B
Check: moves away from B
Energy must increase !
Physics 212 Lecture 13, Slide Physics 212 Lecture 13, Slide 2525
CalculationCalculation
2U Ia B(A) (B) (C) (A) (B) (C)
• What is the potential energy of the final state?
A square loop of side a lies in the x-z plane with current I as shown. The loop can rotate about x axis without friction. A uniform field B points along the +z axis. Assume a, I, and B are known.
z
x
y
B .30˚z
Iinitial final
a
B
1cos(120 )2
oU B B B z
y
B
1cos(120 )2
o
U B
212
U Ia B
2Ia
212
U Ia B44
BIaU 2
23
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