1. A New Topic: Magnetic Fields

2. Chapter 28 and 29
Hour 1: General introduction, Gauss’ Law
Magnetic force (28.1) Cross product of vectors.
Hour 2: Currents create B Fields: Biot-Savart,
B field of loops (magnetic moment). (28.2)
Hour 3: Use Ampere’s Law to calculate B fields (28.3)
Hour 4: Charged particle’s motion in B field. (29.1)
Hour 5: B field force & torque on wires with I (29.2)
Hour 6: Magnetic materials (29.4)

3. Gravitational – Electric Fields
Mass m Charge q (±)
E  k m q
g  G r r2 ˆ rˆ
Create:
e r 2
Fg  mg
FE  qE
Feel:
Also saw… Create:
Dipole p
Feel:
τ  p  E
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4. Magnetism – Bar Magnet
Like poles repel, opposite poles attract
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5. Magnetic Field of Bar Magnet
A magnet has two poles, North (N) and South (S)
Magnetic field lines leave from N, enter at S
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6. 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
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7. Electric Dipole Magnetic Monopoles? p µ 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

8. Fields: Grav., Electric, Magnetic
Mass m Charge q (±)
No Magnetic Monopoles!
E  k m q
g  G r ˆ rˆ
Create: r2
e r 2
Fg  mg
FE  qE
Feel:
Also saw… Create:
Dipole p
E 
Dipole m
 B
Feel:
τ  p  E
τ  m  B

9. What else is magnetic?

10. Magnetic Field of the Earth
Also a magnetic dipole!
North magnetic pole located in southern hemisphere

11. Visualization: Bar Magnet & Earth’s Magnetic Field
( barmag320.html)

12. Magnetic Field B Thus Far…
Bar Magnets (Magnetic Dipoles)…
Create: Dipole Field
Feel: Orient with Field
Does anything else create or feel a magnetic field?

13. Moving Charges Feel Magnetic Force
FB  q v  B
Magnetic force perpendicular both to: Velocity v of charge and magnetic field B

14. Magnetic Field B: Units
FB  q v  B
Since
B Units  newton  1 N  1 N
coulombmeter/second
C m s A  m
This is called 1 Tesla (T)
1 T = 104
Gauss (G)

15. Recall: Cross Product

16. Notation DemonstrationX
OUT of page “Arrow Head”
INTO page “Arrow Tail”

17. Cross Product: Magnitude
Computing magnitude of cross product A x B:
C  AxB
C  A B sin
|C |:
area of parallelogram

18. Cross Product: Direc tion
C  AxB
Right Hand Rule #1:
Curl fingers of right hand in the direction that moves A (green vector) to B (red vector) through the smallest angle
Thumb of right hand will point in direction of the cross product C (orange vector)
ions/vectorfields/14-CrossProduct/14- crossprod320.html

19. ˆi  ˆj  kˆ ˆj kˆ  ˆi kˆ  ˆi  ˆj ˆj ˆi  kˆ ˆi  kˆ  ˆj
Cross Product: Signs
ˆi  ˆj  kˆ
ˆj kˆ  ˆi kˆ  ˆi  ˆj
ˆj ˆi  kˆ
kˆ  ˆj  ˆi
ˆi  kˆ  ˆj
Cross Product is Cyclic (left column) Reversing A & B changes sign (right column)

20. PRS Questions: Right Hand Rule

21. FB  q v  B FE  qE F  q E  v  B
Putting it Together: Lorentz Force
C harges Fee l…
FE  qE
FB  q v  B
Magnetic Fields
Electric Fields
F  q E  v  B
This is the final word on the force on a charge

22. Application: Velocity Selector
What happens here?

23. Fnet Velocity Selector E  q(E  v  B)  0  v  B
Particle moves in a straight line when
Fnet E
 q(E  v  B)  0  v  B

24. PRS Question: Hall Effect