1. Today’s Concept: Torques in Magnetic Fields
Physics 2112 Unit 13
Today’s Concept:
Torques in Magnetic Fields
Unit 13, Slide 1

2. Force on current carrying wire
Last Time: y z x B F I
This Time:
Unit 13, Slide 2

3. 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.
What is the force on the wire?
X X X X X X X I
0.5m
Unit 13, Slide 3

4. Value of Torque |t| = 2*(W/2)*sin(Q)*(B*L) = W*L*B*sin(Q)
= (Area of Loop)*B*sin(Q) z . B Q W
final

5. Magnetic Dipole Moment
Define: Area vector
Magnitude = Area
Direction uses R.H.R.
Define: Magnetic Dipole moment
Unit 13, Slide 5

6. m Makes Torque Easy! The torque always wants to line m up with B! m m
turns m toward B x y z B m
turns m toward B x y z
“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| = |m||B|sinq
Unit 13, Slide 6

7. 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

8. Magnetic Field can do Work on Current
From Physics 2111:
From Physics 2112: B m
Define U = 0 at position of maximum torque
Unit 13, Slide 8

9. 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 ?
Biggest when
Unit 13, Slide 9

10. CheckPoint 2B Which orientation has the most potential energy?
Unit 13, Slide 10

11. 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

12. Example 13.3 (Rotating Loop)z 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. B . B
30˚ y y
How much does the potential energy of the system change as the coil moves from its initial position to its final position. a I x
final
initial
Conceptual Analysis
A current loop may experience a torque in a constant magnetic field
t = m X B
We can associate a potential energy with the orientation of loop
U = - m ∙ B
The purpose of this Check is to jog the students minds back to when they studied work and potential energy in their intro mechanics class.
Strategic Analysis
Find m
Calculate the change in potential energy from initial to final
Unit 13, Slide 12

13. Electric Dipoles Magnetic Dipoles
Remember?
Electric Dipoles
Magnetic Dipoles + -

14. What’s all this good for?
Many things. I’ll mention two…..
one every day…..
one high tech X . X .
What if when it reaches this point, you reverse the direction of the current in the coil?
Electric Motor

15. Magnetic Resonance Imaging (MRI)
Protons have charge and spin…have magnetic moment
Place in strong B field and m will try to align with field. m
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)