1. Chap 21 & 22: Magnets & Magnetic Fields

3. objectives Did this will do this Charges
Force between charges & Electric Field
Moving charges, current
will do this
Magnetic Field
Force on moving charges in magnetic field
Generation of magnetic field by moving charges
Generation of current by moving magnetic field

5. Examples of Magnets Compass Earth Hi-Fi speakers Fridge magnets
Electric motors
Scrap yards
Cupboard doors
video/audio tapes

7. Properties of magnets
As with charges we find that there are attractive and repulsive forces.
We find that magnets stick to certain non-magnetised materials
We find that magnets can both attract and repel each other

12. EARTH’S MAGNETIC FIELD

19. Aurora Movie

20. Magnetic Induction
Magnetism can be induced in materials by rubbing with another magnetised material
Ferromagnetic materials such as iron, cobalt, gadolinium and dysprosium can become permanently magnetic
Paramagnetic materials such as steel can become magnetised but this will only last for a short time

21. Magnetic Induction
A permanent magnetised ferromagnet can thus be attracted to paramagnetic material by inducing magnetism in that material

23. Magnets are Cool! North Pole and South Pole Magnetic Field Lines
Opposites Attract
Likes Repel
Magnetic Field Lines
Arrows give direction
Density gives strength
Looks like dipole! + -
Lets Break it!

24. Permanent Magnets North Pole and South Pole Magnetic Field Lines
Opposites Attract
Likes Repel
Magnetic Field Lines
Arrows give direction
Density gives strength
Looks like dipole!
Lets Break it!

25. Field Lines of Bar Magnet
S N
Complete the lines

26. Magnetic Poles In electrostatics there are two types of charges:
positive and negative
Similarly there are two types of “poles”:
North and South
Like poles repel
Dislike poles attract
By convention:
The North pole of a compass needle points to the geographical north pole.

27. Quick Quiz
North
The Geographical North pole is defined where the axis of rotation of the earth goes through the arctic
Is this:
Exactly the north magnetic pole
Nearly the north magnetic pole
Exactly the south magnetic pole
Nearly the south magnetic pole

28. Monopoles A north pole is always found with a corresponding south pole
Unlike with electric charge no isolated magnetic pole or monopole has ever been discovered
A north pole is always found with a corresponding south pole

29. No Magnetic Charges
Magnetic Fields are created by moving electric charge!
Where is the moving charge?
Orbits of electrons about nuclei
Intrinsic “spin” of electrons (more important effect)

30. Magnetic Field
Magnetic Field like the Electric Field is another example of a vector field
It is defined everywhere
It has a magnitude
Units:
Tesla (T)
It has a direction, the direction that a compass needle would point

31. Magnetic Field Lines
If we move a compass around and record the direction it points everywhere we can map out the direction of the magnetic field lines

32. Magnetic Field Lines

33. Magnetic Field Lines
Experiments of Pierre de Maricourt mapped out the field lines on naturally magnetic sphere
Demonstrated that they all pointed to two diametrically opposed points or “poles”.

34. Moving charges in a magnetic field
Moving charges in a magnetic field experience a magnetic force

35. Magnetic Field N S N S
Magnetic Field, B, is in direction compass needle points
Magnitude is defined in terms of force on moving charges

36. Moving charge in magnetic fieldB B B FB v +
Experiments show

37. Electric vs Magnetic Field Lines
Similarities
Density gives strength
Arrow gives direction
Leave +, North
Enter -, South
Differences
Start/Stop on electric charge
No Magnetic Charge, lines are continuous!

38. Difference between Electric & Magnetic Forces
acts in the direction of the electric field
acts on a charged particle regardless of whether the particle is moving
does work in displacing the particle
acts perpendicular to the magnetic field
acts on a charged particle only when the particle is moving
does no work in displacing the particle

39. Force on a moving charge
The result of all of these experiments can be summarised by this equation
We can use this relationship to define the magnitude of B
Units:
Tesla (T)

40. Magnetic force does no work in displacing a moving particle
Work & Energy
Magnetic force does no work in displacing a moving particle
Kinetic energy
of particle cannot
change
speed cannot change
but velocity and
direction can

41. Charged particle in uniform magnetic field
Magnetic field into board +
Note speed never changes + +
but direction does v FB + +
Force is always  to v + + v

42. Charged particle in uniform magnetic field
Magnetic field into board
Since force is always radial it acts to keep particle moving in a circle + v FB +

44. Right hand rule

45. Review RHR Force on moving (+) charge in Magnetic field
Thumb….. gives F on + charge
fingers……. I(or v),
palm….. B (field) B I F + v
Magnetic field produced by moving charge.
Thumb I, fingers where you want it, palm gives B x •
Thumb out, fingers up, palm left.
Palm out of page.

48. Direction of Magnet Force on Moving Charges
Velocity B Force
out of page right
out of page left
out of page top
out of page down
Right Hand Rule
Thumb ___, Fingers ___, palm ___
Negative charge has opposite F!

49. Preflight What is the direction of the magnetic field in region 1?
Each chamber has a unique magnetic field. A positively charged particle enters chamber 1 with velocity 75 m/s up, and follows the dashed trajectory. 1 2
v = 75 m/s
q = +25 mC
What is the direction of the magnetic field in region 1?
1) up
2) down
3) left
4) right
5) into page
6) out of page

50. Force on moving charge in magnetic Field
The magnitude of the magnetic force FB exerted on the particle is proportional to the charge q and to the speed of the particle v
The magnitude and direction of the force FB depend on the velocity of the particle v and the magnitude and direction of the magnetic field B

51. Force on moving charge in magnetic Field
When the particle moves parallel to the magnetic field vector, the magnetic force acting on the particle is zero
When the particle’s velocity vector v makes an angle   0 with the magnetic field the magnetic force acts in a direction perpendicular to both v and B i.e. F is  to the plane formed by v and B

52. Force on moving charge in magnetic Field
The magnetic force exerted on a positive charge is in the opposite direction of the force exerted on a negative charge moving in the same direction
The magnitude of the magnetic force exerted on the moving particle is proportional to sin q where q is the angle the particles velocity vector makes with the direction of B

53. Charged particle in uniform magnetic field
velocity
Bubble chamber
angular velocity
Mass spectrometer

54. Direction of Magnet Force on Moving Charges
Velocity B Force
out of page right
out of page left
out of page up
out of page down
Right Hand Rule
Thumb ___, Fingers ___, palm ___
Negative charge has opposite F!

55. Preflight What is the direction of the magnetic field in region 1?
Each chamber has a unique magnetic field. A positively charged particle enters chamber 1 with velocity 75 m/s up, and follows the dashed trajectory. 1 2
v = 75 m/s
q = +25 mC
What is the direction of the magnetic field in region 1?
1) up
2) down
3) left
4) right
5) into page
6) out of page

56. Magnitude of Magnet Force on Moving Chargesq
The magnetic force on a charge depends on the magnitude of the charge, its velocity, and the magnetic field.
F = q v B sin(q)
Direction from RHR
Thumb (v), fingers (B), palm (F)
Note if v is parallel to B then F=0 B

57. Example
The three charges below have equal charge and speed, but are traveling in different directions in a uniform magnetic field.
1) Which particle experiences the greatest magnetic force?
1) 1 2) 2 3) 3 4) All Same
2) The force on particle 3 is in the same direction as the force on particle 1.
1) True 2) False B 3 2 1

58. Electric vs Magnetic Electric Magnetic Source: Charges Moving Charges
Act on: Charges Moving Charges
Magnitude: F=Eq F = q v B sin(q)
Direction: Parallel E Perpendicular to v,B

59. Velocity Selector x x x x x x x x x x x x
Determine magnitude and direction of magnetic field such that a positively charged particle with initial velocity v travels straight through and exits the other side.
x x x x x x x x x x x x E v
What do you need to change if want to select particles with a negative charge?

60. Motion of q in uniform B field
x x x x x x x
Force is perpendicular to B,v
Force is perpendicular to B,v
B does no work! (W=F d cos q )
Speed is constant (W=D K.E. )
Circular motion v R F
Calculate R
Uniform B into page

61. Preflight What is the speed of the particle in chamber 2.
Each chamber has a unique magnetic field. A positively charged particle enters chamber 1 with velocity v1=75 m/s up, and follows the dashed trajectory. 1 2
v = 75 m/s
q = +25 mC
What is the speed of the particle in chamber 2.
1) v2 < v1
2) v2 = v1
3) v2 > v1

62. Preflight
Each chamber has a unique magnetic field. A positively charged particle enters chamber 1 with velocity 75 m/s up, and follows the dashed trajectory. 1 2
v = 75 m/s
q = +25 mC
Compare the magnitude of the magnetic field in chambers 1 and 2
1) B1 > B2
2) B1 = B2.
3) B1 < B2

63. Solenoids Magnitude of Field inside of solenoid : B=m0 n I
n is the number of turns of wire/meter on solenoid.
Direction Thumb direction of I, fingers point toward center, palm gives direction of B.

64. What is the net force between the two solenoids?
a)Attractive
b) Zero
b)Repulsive
Look at field lines, opposites attract.
Look at currents, same direction attract.