1. W07D1 Magnetic Dipoles, Force and Torque on a Dipole, Experiment 2
W07D1 Magnetic Dipoles, Torque and Force on a Dipole, Experiment 2: Magnetic Dipole in a Helmholtz Coil
Reading Course Notes: Sections 8.4, 8.6.4, , 8.13, 9.5, 9.9
Class 18

2. Announcements Exam Two Reviews: Monday from 7-9 pm in 26-152
Tuesday from 9-11 pm in
Wednesday from 9-11 pm in
PS 6 due W07 Tuesday at 9 pm in boxes outside or
Exam 2 Thursday March 21 7:30 - 9:30 pm: See announcement pages for section room assignments
Conflict Friday March am in ; noon in 6-120
Class 15

3. Magnetic Field of Bar Magnet
(1) A magnet has two poles, North (N) and South (S)
(2) Magnetic field lines leave from N, end at S
Class 12

4. Magnetism – Bar Magnet Like poles repel, opposite poles attract
Class 12

5. Bar Magnets Are Dipoles!
Create Dipole Field
Rotate to orient with Field
Is there magnetic “mass” or magnetic “charge?”
NO! Magnetic monopoles do not exist in isolation
Class 12

6. Magnetic Monopoles? Electric Dipole Magnetic Dipole -q q When cut:
2 monopoles (charges)
When cut: 2 dipoles
Magnetic monopoles do not exist in isolation
Another Maxwell’s Equation! (2 of 4)
Gauss’s Law
Magnetic Gauss’s Law
Class 12

7. Conservation of Magnetic Flux:
Class 12

8. Torque on a Current Loop in a Uniform Magnetic Field
Class 18

9. Review: Magnetic Force on Current-Carrying Wire
If the wire is a uniform magnetic field then
If the wire is also straight then
Class 18

10. Group Problem: Current Loop
Place rectangular current loop in uniform B field
1) What is the net force on this loop?
2) What is the net torque on this loop?
3) Describe the motion the loop makes
Class 18

11. Torque on Rectangular Loop
Area vector x
No net force but there is a torque
Class 18

12. Magnetic Dipole Moment
Class 15

13. Torque on Current Loop
Place rectangular current loop in uniform B field
Magnetic moment points out of the page
torque tries to align the magnetic moment vector in the direction of the magnetic field
Class 18

14. Concept Question: Magnetic Field Lines
The picture shows the field lines outside a permanent magnet The field lines inside the magnet point: Up
Down
Left to right
Right to left
The field inside is zero
I don’t know
Class 15

15. Concept Q. Answer: Magnetic Field Lines
Answer: 1. They point up inside the magnet
Magnetic field lines are continuous.
E field lines begin and end on charges.
There are no magnetic charges (monopoles) so B field lines never begin or end
Class 15

16. Demonstration: Deflection of a Compass Needle by a Magnet G1
Class 12

17. Demonstration: Galvanometer principle G10
Class 18

18. Concept Question: Dipole in Fieldm
From rest, the coil above will:
rotate clockwise, not move
rotate counterclockwise, not move
move to the right, not rotate
move to the left, not rotate
move in another direction, without rotating
both move and rotate
neither rotate nor move
I don’t know
Class 18

19. Concept Q. Answer: Dipole in Field
Answer: 1. Coil will rotate clockwise (not move)
No net force so no center of mass motion. BUT Magnetic dipoles rotate to align with external field (think compass)
Class 18

20. Force on a Dipole in a Non-Uniform Field
Class 18

21. Dipoles don’t move??? This dipole rotates but doesn’t feel a net force
in a uniform magnetic field
But dipoles can feel magnetic force.
Class 18

22. Dipoles in Non-Uniform Fields: Magnetic Force
Class 18

23. Concept Question: Dipole in Field
The current carrying coil above will feel a net force
upwards
downwards
of zero
I don’t know
Class 18

24. Concept Q. Answer: Dipole in Field
Answer: 2. Feels downward force. The forces shown produce a net downward force
Class 18

25. Force on Magnetic DipoleS m N S
What makes the field pictured? Bar magnet below dipole, with N pole on top. It is aligned with the dipole pictured, they attract!
Class 18

26. Work Done by Interaction to Anti-align Magnetic Dipole
\begin{vmatrix}\vec{\tau}\end{vmatrix} = \mu B \sin \theta
W = -\int_0^\pi \tau d\theta = -\int_0^\pi \mu B \sin \theta \,d\theta
Class 15

27. Potential Energy: Dipole in Magnetic Field
Set zero reference point
Lowest energy state (aligned) :
Highest energy state (anti-aligned):

28. Force on Magnetic DipoleS N S
along z-axis
Class 18

29. Magnetic Field Profiles Experiment 2
Week 08, Day 2
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Magnetic Field Profiles Experiment 2
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30. Concept Question: Dipole in Helmholtz
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Concept Question: Dipole in Helmholtz
A dipole pointing along the positive x-direction and located at the center of a Helmholtz coil will feel:
a force but not a torque.
a torque but not a force.
both a torque and a force.
neither force nor torque.
Class 19
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31. Concept Q. Answer: Dipole in Helmholtz
Week 08, Day 2
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Concept Q. Answer: Dipole in Helmholtz
Answer: 2. a torque but not a force. The Helmholtz coil makes a UNIFORM FIELD.
Dipole feels only torque (need gradient for force).
Class 19
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32. Concept Question: Dipole in Anti-Helmholtz Coil
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Concept Question: Dipole in Anti-Helmholtz Coil
A dipole pointing along the positive z-direction and located at the center of an anti- Helmholtz coil will feel:
a force but not a torque.
a torque but not a force.
both a torque and a force.
neither force nor torque.
Class 19
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33. Concept Q. Answer: Dipole in Anti-Helmholtz Coil
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Concept Q. Answer: Dipole in Anti-Helmholtz Coil
Answer: 1. A force because there is a gradient in the magnetic field but no torque because the magnetic field at the center is zero.
Class 19
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34. Experiment 2: Magnetic Forces on Dipole in Fields of Helmholtz Coil
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Experiment 2: Magnetic Forces on Dipole in Fields of Helmholtz Coil
Class 19
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35. Getting Started: Set up current supply
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Getting Started: Set up current supply
Open circuit (disconnect a lead)
Turn current knob full CCW (off)
Increase voltage to ~12 V
This will act as a protection: V<12 V
Reconnect leads in Helmholtz mode
Increase current to ~1 A
Class 19
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36. Week 08, Day 2
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Appendix Experiment 2: Magnetic Forces on Dipole in Fields of Helmholtz Coil Field Configurations and Concept Questions
Class 19
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37. Appendix 2: Gauss’s Law for Magnetism
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Appendix 2: Gauss’s Law for Magnetism
Class 19
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38. Animation: Magnetic Field Generated by a Current Loop
Class 18

39. Demonstration: Magnetic Field Lines from Bar Magnet G2
Class 12