Your Comments
Electricity & Magnetism Lecture 13, Slide 1
i don't understand how to use magnetic dipole moment at all
Those eyes in the prelecture look so sad, even though the physics is so exciting.
Can you PLEASE go over RC Circuits again because it doesn't really make sense to me
How do we chose a direction on the vector length L? Is it arbitrary?
I did not understand the dipole moment and potential energy part. Also can you please clarify how to find direction of things using various right hand rules. I'm getting confused!
Today (26 Feb) is my birthday, so I wanted to send out a message to celebrate my 19th.
Torque was hard in 211...I don't even want to think about it in 212 :(
Is the area (A) in the equation (for dipole moment and torque) actually the cross sectional area?
So is it just the amount of area that the magnetic field passes through? Or is it the total area
enclosed by the loop?
You know, I don't say this often, but this magnetism stuff is kind of interesting. Almost makes me wish I wasn't a bioengineer and I was an ECE major. Almost.
You know, I really wish the homework was do-able without arcane mastery of geometry...
Last Time:
F qv B
Electricity & Magnetism Lecture 13, Slide 3
yz
x
BF
I
This Time:
BvqFi
i
BvqNF avg
BLIF
avgqnAvI
nALN
What is the force on section d-a of the loop?A) ZeroB) Out of the pageC) Into the page
Clicker Question
Electricity & Magnetism Lecture 13, Slide 6
BLIF
What is the direction on the net force on the loop?
A. Out of the page B. Into of the page
C. The net force on the loop is zero
CheckPoint 1a
“it is a closed loop (length vector is 0) so the net forceis 0 F = ILxB = 0
Electricity & Magnetism Lecture 13, Slide 7
A square loop of wire is carrying current in the counterclockwise direction. There is a
horizontal uniform magnetic field pointing to the right.
CheckPoint 1b
In which direction will the loop rotate? (assume the z axis is out of the page)
A) Around the x axisB) Around the y axisC) Around the z axisD) It will not rotate
x
y
Electricity & Magnetism Lecture 13, Slide 8
What is the direction of the net torque on the loop?
A. Up B. Down
C. Out of the page D. Into the page
E. The net torque is zero
CheckPoint 1c
RF
Electricity & Magnetism Lecture 13, Slide 9
FR
r x f = torque
Magnetic Dipole Moment
Area vector
Magnitude = Area
Direction uses R.H.R.
Magnetic Dipole moment
ANI
Electricity & Magnetism Lecture 13, Slide 10
EXPLAIN THE MAGNETIC DIPOLE... What IS IT?!?!?!?!!?!?!
Makes Torque Easy!
The torque always wants to line up with B!
Electricity & Magnetism Lecture 13, Slide 11
B
B
turns toward B
x
y
z
B
B
turns toward Bx
y
z
B
Practice with and
B
In this case is out of the page (using right hand rule)
I
Electricity & Magnetism Lecture 13, Slide 12
B
B
x
y
z
is up (turns toward B)B
CheckPoint 2a
Electricity & Magnetism Lecture 13, Slide 13
B
Biggest when B
Three 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?
Magnetic Field can do Work on Current
From Physics 211:
From Physics 212: sin( )B B
dW
Define U 0 at position of maximum torque
BU
Electricity & Magnetism Lecture 13, Slide 14
-1.5
-1
-0.5
0
0.5
1
1.5
0 30 60 90 120 150 180
B
WU
sin( ) cos( )W B d B B
Physics 212 Lecture 13, Slide 16
ACT
30
c
a
fa
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
BY YOU
BY FIELD
c
a
fa
fifieldby UUUW _
BU
CheckPoint 2c
Electricity & Magnetism Lecture 13, Slide 17
C): )cos1()cos(_ ccfieldby BBBW
B): BBW fieldby 0_
A): )cos1()cos(_ aafieldby BBBW f +
Three different orientations of a magnetic dipole moment in a constant magnetic field are
shown below. In order to rotate a horizontal magnetic dipole to the three positions shown,
which one requires the most work done by the magnetic field?
How much does the potential energy of the system change as the coil moves from its initial position to its final position.
Conceptual AnalysisA current loop may experience a torque in a constant magnetic field
X BWe can associate a potential energy with the orientation of loop
U ∙ B
z
x
y
B .30˚
y
z
I
initialfinal
Strategic AnalysisFind Calculate the change in potential energy from initial to final
a
B
Calculation
A square loop of side a lies in the xz plane with current I as shown. The loop can rotate about xaxis without friction. A uniform field B points along the +z axis. Assume a, I, and B are known.
Electricity & Magnetism Lecture 13, Slide 18
What is the direction of the magnetic moment of this current loop in its initial position?
A) +x B) x C) +y D) y
z
x ●y
A square loop of side a lies in the xz plane with current I as shown. The loop can rotate about xaxis without friction. A uniform field B points along the +z axis. Assume a, I, and B are known.
xinitial
final
z
x
y
B .30˚
y
z
I
initialfinal
a
B
Calculation
Electricity & Magnetism Lecture 13, Slide 19
AL
z
y
.
X
Right Hand Rule
AL
What is the direction of the torque on this current loop in the initial position?
A) +x B) x C) +y D) y
y
B
z
y
z
x
y
B .30˚
y
z
I
initialfinal
a
B
Calculation
A square loop of side a lies in the xz plane with current I as shown. The loop can rotate about xaxis without friction. A uniform field B points along the +z axis. Assume a, I, and B are known.
Electricity & Magnetism Lecture 13, Slide 20
Calculation
What is the potential energy of the initial state?
A) Uinitial < 0 B) Uinitial 0 C) Uinitial > 0
z
y
B
z
x
y
B .30˚
y
z
I
initialfinal
a
BA square loop of side a lies in the xz plane with current I as shown. The loop can rotate about xaxis without friction. A uniform field B points along the +z axis. Assume a, I, and B are known.
BU
0 B
Electricity & Magnetism Lecture 13, Slide 21
090
What is the potential energy of the final state?
A) Ufinal < 0 B) Ufinal 0 C) Ufinal > 0
y
initial
initial final
z
y
B
90o
z
y
B
90o + 30o
Check: moves away from B
z
x
y
B .30˚
y
z
I
initialfinal
a
B
Calculation
A square loop of side a lies in the xz plane with current I as shown. The loop can rotate about xaxis without friction. A uniform field B points along the +z axis. Assume a, I, and B are known.
BU
Energy must increase !
Electricity & Magnetism Lecture 13, Slide 22
0> BU
0< B
0120
A) B) C)
What is the potential energy of the final state?
z
x
y
B .30˚
y
z
I
initialfinal
a
B
Calculation
A square loop of side a lies in the xz plane with current I as shown. The loop can rotate about xaxis without friction. A uniform field B points along the +z axis. Assume a, I, and B are known.
BU
BIaU 2
2
3
Electricity & Magnetism Lecture 13, Slide 23
BIaU 2
2
1BIaU 2
z
y
B
120o
2
1)120(cos
2Ia
BBBU o 2
1)120(cos
BIaU 2
2
1
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