Your Comments
You know, I really wish the homework was do-able without arcane mastery of geometry...
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.
Electricity & Magnetism Lecture 13, Slide 1
Physics 212
Lecture 13
Today’s Concept:
Torques
Electricity & Magnetism Lecture 13, Slide 2
Last Time:
F  qv  B
This Time:

 
F  q  vi  B
z
F
i



F  qNvavg  B
N  nAL
y

 
F  IL  B
B
I
x
I  qnAvavg
Electricity & Magnetism Lecture 13, Slide 3
Clicker Question

 
F  IL  B
A A.
B B.
C C.
Electricity & Magnetism Lecture 13, Slide 4
Clicker Question

 
F  IL  B
A A.
B B.
C C.
Electricity & Magnetism Lecture 13, Slide 5
Clicker Question

 
F  IL  B
What is the force on section d-a of the loop?
A) Zero
B) Out of the page
C) Into the page
Electricity & Magnetism Lecture 13, Slide 6
CheckPoint 1a
A square loop of wire is carrying current in the counterclockwise direction. There is a
horizontal uniform magnetic field pointing to the right.
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
“it is a closed loop (length vector is 0) so the net force
is 0 F = ILxB = 0
Electricity & Magnetism Lecture 13, Slide 7
CheckPoint 1b
y
x
In which direction will the loop rotate?
(assume the z axis is out of the page)
A)
B)
C)
D)
Around the x axis
Around the y axis
Around the z axis
It will not rotate
Electricity & Magnetism Lecture 13, Slide 8
CheckPoint 1c
R
F
 
  R F

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
r x f = torque
Electricity & Magnetism Lecture 13, Slide 9
Magnetic Dipole Moment
EXPLAIN THE MAGNETIC DIPOLE... What IS IT?!?!?!?!!?!?!
Area vector
Magnitude = Area
Direction uses R.H.R.
Magnetic Dipole moment

  NIA

Electricity & Magnetism Lecture 13, Slide 10
 Makes Torque Easy!

  B


z

The torque always wants to line  up with B!

    B turns  toward B


z
y
B

x
y
x
B
   turns  toward B
  B
Electricity & Magnetism Lecture 13, Slide 11
Practice with  and 

  B


I
B

In this case  is out of the page (using right hand rule)
z

x

    B is up (turns  toward B)


y
B
Electricity & Magnetism Lecture 13, Slide 12
CheckPoint 2a
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?

  B



Biggest when   B

Electricity & Magnetism Lecture 13, Slide 13
Magnetic Field can do Work on Current
From Physics 211:
W   d
From Physics 212:
    B   B sin( )
W    B sin( )d   B cos( )    B
1.5
U  W
Define U  0 at position of
maximum torque
 
U    B
1
0.5
0
0
-0.5
-1
-1.5
30
60
90
120
150
180

B
Electricity & Magnetism Lecture 13, Slide 14
CheckPoint 2b
f

U  +Bcosf
U0
U  Bcos
 
U    B
Electricity & Magnetism Lecture 13, Slide 15
ACT
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.
fa
a
c
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)
B)
C)
D)
30
Wyou > 0, Wfield > 0
Wyou > 0, Wfield < 0
Wyou < 0, Wfield > 0
Wyou < 0, Wfield < 0
W field  U
• U > 0, so Wfield < 0. Wyou must be opposite Wfield
• Also, torque and displacement in opposite directions 
Wfield < 0
Physics 212 Lecture 13, Slide 16
CheckPoint 2c
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?
fa
BY
YOU
a
c
BY
FIELD
Wby _ field  U  Ui  U f
 
U    B
C):
Wby _ field  B  (B cos c )  B(1  cos c )
B):
Wby _ field  B  0  B
A):
Wby _ field  B  (B cos a )  B(1 + cos fa )
Electricity & Magnetism Lecture 13, Slide 17
Calculation
z
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
B
30˚
.
y
y
a
How much does the potential energy of the
system change as the coil moves from its
initial position to its final position.
B
I
x
final
initial
Conceptual Analysis
A current loop may experience a torque in a constant magnetic field
XB
We can associate a potential energy with the orientation of loop
U∙B
Strategic Analysis
Find 
Calculate the change in potential energy from initial to final
Electricity & Magnetism Lecture 13, Slide 18
Calculation
z
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


LA +z axis. Assume a, I, and B are known.
along the
z
B
30˚
.
y
y
a
I
x
B
final
final
initial
initial
What is the direction of the magnetic moment of this current loop in its initial
position?
A) +x
B) x
z
z
C) +y
D) y
.
x
●

  LA


y
y
X
Right Hand Rule
Electricity & Magnetism Lecture 13, Slide 19
Calculation
z
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
B
30˚
.
y
B
y
a
I
x
final
initial
What is the direction of the torque on this current loop in the initial position?
A) +x
B) x
C) +y
D) y
z
B
y
Electricity & Magnetism Lecture 13, Slide 20
Calculation
z
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.
 
U    B
z
B
30˚
.
y
B
y
a
I
x
final
initial
What is the potential energy of the initial state?
A) Uinitial < 0
B) Uinitial  0
C) Uinitial > 0
z
  90
0
B

 
B 0

y
Electricity & Magnetism Lecture 13, Slide 21
Calculation
z
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.
 
U    B
z
B
30˚
.
B
y
y
a
I
x
final
initial
initial
What is the potential energy of the final state?
A) Ufinal < 0
B) Ufinal  0
C) Ufinal > 0
Check:  moves away from B
z
z
initial
final
B
B
  90o + 30o
  90o

y
y

Energy must increase !
  1200
 
B<0
 
U    B > 0
Electricity & Magnetism Lecture 13, Slide 22
Calculation
z
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.
 
U    B
z
B
30˚
.
y
B
y
a
I
x
final
initial
What is the potential energy of the final state?
B) U 
A) U  Ia2 B
z
cos (120 )  
B
  120o

y
1
2
3 2
Ia B
2
C)
U
1 2
Ia B
2
 
1
U     B  B cos (120o )  B
2
2
  Ia
1
U  Ia 2 B
2
Electricity & Magnetism Lecture 13, Slide 23