Physics 2112
Unit 13
Today’s Concept:
Torques in Magnetic
Fields
Unit 13, Slide 1
Force on current carrying wire
Last Time:
F  qv  B
This Time:

 
F  q vi  B
i



F  qNvavg  B
z

 
F  IL  B
y
F
B
I
x
N  nAL
I  qnAvavg
Unit 13, Slide 2
Example 13.1 (Force on Wire)
A wire is carrying 5amps
through a magnetic field
that is 50cm long and has
a strength of 12 Gauss.
X X X X X X X
I
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
What is the force on the
wire?
0.5m

 
F  IL  B
Unit 13, Slide 3
Value of Torque
|t| = 2*(W/2)*sin(Q)*(B*L)
= W*L*B*sin(Q)
= (Area of Loop)*B*sin(Q)
z
Q
.
W
final
B
Magnetic Dipole Moment
Define: Area vector
Magnitude = Area
Direction uses R.H.R.
Define: Magnetic Dipole moment

  NIA

Unit 13, Slide 5

Makes Torque Easy!

t  B


z
The torque always wants to line 
up with B!

t    B turns  toward B

z



x
y
y
B
x
B

t    B turns  toward B


“Dipole moments, I don't get how they are different from
torques”
Dipole moments tell you how much torque a
given B field will place on a loop. |t| = |||B|sinq
Unit 13, Slide 6
Example 13.2 (Torque on Loops)
5A of current is moving
clockwise through 20
loops of copper wire.
The loops have a radius
of 50cm and are placed
in a 500 Gauss magnetic
field as shown to the
right.
What is the torque on the
loop?
Unit 13, Slide 7
Magnetic Field can do Work on Current
From Physics 2111:
W   t dq
From Physics 2112:
t    B   B sin(q )
 
W    B sin(q )dq  B cos(q )    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
Unit 13, Slide 8
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 ?

t  B


Biggest when

B

Unit 13, Slide 9
CheckPoint 2B
Which orientation has the most potential energy?
 
U    B
Unit 13, Slide 10
CheckPoint 2C
In order to rotate a horizontal magnetic dipole to the
three positions shown, which one requires the most
work done by the magnetic field?
Unit 13, Slide 11
Example 13.3 (Rotating Loop)
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˚
.
B
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.
I
x
initial
final
Conceptual Analysis
A current loop may experience a torque in a constant magnetic field
t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
Unit 13, Slide 12
Remember?
Electric
Dipoles


U    elec  E

 
t   elec  E
+

 elec
-

 qd
Magnetic
Dipoles

U    mag  B


t   mag  B




 mag  NIA
What’s all this good for?
Many things. I’ll mention two…..
one every day…..
one high tech
X
.
Electric
Motor
What if when it reaches this
point, you reverse the
direction of the current in
the coil?
MRI
Protons have charge and spin…have
magnetic moment Place in strong B field and m

will try to align with field.
Will precess like top in gravity
field (…remember from 2111?)
Look for the signal from the
precession and can spot
protons in hydrogen
Hydrogen is in water which is in soft tissue
Magnetic Resonance Imaging (MRI)