1. PHY 102: Lecture 6 6.1 Magnetic Field
6.2 Magnetic Force on Moving Charges
6.3 Magnetic Force on Currents
6.4 Magnetic Field Produced by Current

2. PHY 102: Lecture 6 Magnetic Force Magnetic Fields
6.1
Magnetic Field

3. Basics of This Chapter Charge moving in a magnetic field feels a force
Moving charge creates a magnetic field

4. Magnetic Field Into and Out of Page

5. Magnetic Poles North magnetic pole
The end of the needle that points north
South magnetic pole
The opposite end
No one has been able to separate magnetic poles
Electric charges can be separated

6. Magnetic Force / Field Direction of the magnetic force
Like poles repel each other
Unlike poles attract each other
Surrounding a magnetic, there is a magnetic field
Direction of the magnetic field
Direction indicated by the north pole of a small compass needle
Magnetic field lines
To visualize the electric field, we introduced electric field lines
It is possible to draw magnetic field lines
The lines originate from north pole, and end on the south pole
They do not end in midspace
The strength of the field is proportional to the number of lines per unit area that passes through a surface oriented perpendicular to the lines

7. Magnetic Pole Force Directions - 1

8. Magnetic Pole Force Directions - 2
At any location in the vicinity of a magnet, the north pole of a small compass needle points in the direction of the magnetic field at that location

9. Magnetic Field Lines

10. Earth’s North Magnetic Pole
The compass and field lines point to the earth’s north magnetic pole
Therefore, the earth’s north magnetic pole is actually a south pole

11. PHY 102: Lecture 6 Magnetic Force Magnetic Fields
6.2
Magnetic Force on Moving Charge

12. Magnetic Field Force on Moving Charge
Two conditions must be met for a charge to experience a magnetic force when placed in a magnetic field
The charge must be moving
The velocity of the moving charge must have a component that is perpendicular to the direction of the magnetic field

13. No Force – Velocity Parallel to Magnetic Field

14. Max Force – Velocity Perpendicular to Magnetic Field

15. Some Force – Velocity at Angle to Magnetic Field

16. Direction of Magnetic Force Right-Hand Rule No. 1
Extend the right hand so the fingers point along the direction of the magnetic field B
The thumb points along the velocity v of the charge
The palm of the hand then faces in the direction of the magnetic force F that acts on a positive charge
If the moving charge is negative, the direction of the magnetic force is opposite to that predicted by RHR-1

17. Illustration of Right-Hand Rule No. 1

18. Definition of Magnetic Field
The magnitude B of the magnetic field at any point in space is defined as
F is the magnitude of magnetic force on a test charge
|q0| is the magnitude of the test charge
v is the magnitude of the charge’s velocity
v makes an angle  (0 <=  <= 1800) with the direction of the magnetic field
The magnetic field B is a vector, and its direction can be determined by using a small compass needle
SI Unit of Magnetic Field = 1 tesla (T)

19. Problem 1 - 1
A proton in a particle accelerator has a speed of 5.0 x 106 m/s
The proton encounters a magnetic field whose magnitude is 0.40 T
Direction of the field makes and angle of q = with respect to the protons velocity
(a) Find the magnitude and direction of the magnetic force on the proton
(b) The acceleration of the proton

20. Problem 1 - 2 (a) Positive charge on proton is 1.60 x 10-19 C
Magnitude of force is F = |q0|vB sinq
The direction of the magnetic force is given by RHR-1 and is directed upward

21. Problem 1 - 3 (b) Acceleration if from Newton’s second law
a = F/m = 1.6 x / 9.11 x = 1.8 x 1017 m/s2

22. Compare Particle Motion in Electric and Magnetic Field
Positive charge moving between the plates of a parallel plate capacitor
Initially, the charge is moving perpendicular to the electric field
Direction of the electric force is in the same direction as the electric field
Particle is deflected sideways

23. Compare Particle Motion in Electric and Magnetic Field
Initially, positive charge is moving at right angles to a magnetic field
When the charge enters the field it is deflected upwards by magnetic force
As charge moves upward, the direction of the magnetic force changes
Force always remains perpendicular to the magnetic field and velocity
Charge moves in circle

24. Velocity Selector
Force of the electric field on particle is qE in downward direction
Force of the magnetic field on the moving particle is qvB in the upward direction
The forces are balanced when
qE = qvB
v = E/B
This is the velocity of the particle that will pass straight through the velocity filter from one end to the other

25. Work Done on a Charged Particle Moving Through Magnetic Field
The force is perpendicular to the direction of motion
Therefore, the work done by the magnetic field is zero

26. Circular Trajectory - 1
Velocity of positively charged particle is perpendicular to a constant magnetic field
The magnetic force moves the particle in a circular path
At point 1, the magnetic force F points upward
This force causes the parth to bend upward

27. Circular Trajectory - 2
At point 2, the magnetic force is directed to the left
The magnetic force always remains perpendicular to the velocity
Force is directed toward the center of the circular path

28. Circular Trajectory - 3
Centripetal force equals magnetic force

29. Problem 2 - 1
Proton is released from rest at point A next to positive plate of parallel plate capacitor
Proton accelerates towards the negative plate
Proton leaves capacitor at point B through a small hole
Electric potential of positive plate is 2100 V greater than the negative plate
VA – VB = 2100 V

30. Problem 2 - 2
Outside the capacitor, the proton travels at a constant velocity until it enters a region of constant magnetic field
Field is directed out of the page
B = 0.10 T
Velocity is perpendicular to the magnetic field

31. Problem 2 - 3
(a) Find the speed vB of the proton when it leaves the negative plate of the capacitor
(b) Find the radius r of the circular path on which the proton moves in a magnetic field

32. Problem 2 - 4 (a) Electric force is conservative
Energy is conserved while in capacitor

33. Problem 2 - 5
(b) The radius of curvature of the circular path in the magnetic field is

34. Problem 3 - 1 Bubble-chamber tracks resulting from event at point A
A gamma ray traveling from the left spontaneously transforms into two charged particles
No track from gamma ray
Particles move away from point A producing two spiral tracks
A third charged particle is knocked out of a hydrogen atom and moves forward producing the long track with the slight upward curvature

35. Problem 3 - 2
Each particle has the same mass and a charge of the same magnitude
A uniform magnetic field is directed out of the page
Based on RHR-1 and formula for radius of curved track in magnetic field, we know:
Particles 1 and 3 are –
Particle 2 is +
Particles 1 and 2 are losing energy to hydrogen collisions because tracks spiral inward
Particle 3 has greatest speed

36. Mass Spectrometer - 1

37. Mass Spectrometer - 2 Conservation of energy in electric field
Radius of curvature in magnetic field

38. Mass Spectrometer Output

39. Dr. Molof Thesis Rb 85, 87 Special Spectrometer Scan

40. PHY 102: Lecture 6 Magnetic Force Magnetic Fields
6.3
Magnetic Force on Currents

41. Force on Current in Magnetic Field

42. Problem 4 - 2 Rail Gun Two conducting rails are 1.6 m apart
Rails are parallel to the ground at the same height
A 0.20-kg aluminum rod is lying on top of the rails
A T magnetic field points upward
The field is perpendicular to the ground
There is a current in the rod
The coefficient of static between rod and rails is ms = 0.45

43. How much current is needed to make the rod begin to move?
Problem Rail Gun
How much current is needed to make the rod begin to move?
In what direction will it move?

44. Problem 4 - 3 Rail Gun Friction force = f = msN = msmg
f = 0.45 x 0.20 x 9.8 = N
Magnetic force = ILB = I(1.6)(0.050)
Magnetic force = (0.08)I N
0.882 = 0.08I
I = / 0.08 = 11.0 A
If current is positive RHR-1 give motion to left, negative to the right

45. PHY 102: Lecture 6 Magnetic Force Magnetic Fields
6.4
Magnetic Field Produced by Current

46. Right Hand Rule No. 2
Curl the fingers of the right hand into the shape of a half-circle
Point the thumb in the direction of the conventional current I
The tips of the fingers will point in the direction of the magnetic field B

47. Magnetic Field Long Straight Wire
0 = 4 x 10-7 Tm/A
This is permeability of free space
r is distance from wire

48. Problem 5 - 1 Long straight wire carries current of 3.0 A
Particle charge of +6.5 x 10-6 C
Particle moving parallel to wire at distance of m
Particle speed is 280 m/s
Find magnitude and direction of the magnetic force exerted on the charged particle by the current in the wire.

49. Problem 5 - 2 Magnetic field produced by wire Force on charge
Direction magnetic force is radially inward toward wire (RHR-1)
F =

50. Problem 6 - 1 Two long, parallel, straight wires
Wires separated by m
Current is I1 = 15 A and I2 = 7.0 A
Find the magnitude and direction of force that magnetic field of wire 1 applies to a 1.5 m section of wire 2

51. Problem 6 - 2 Magnetic force on part of wire 2
Magnetic field produced by wire 1
Combined

52. Problem 6 - 3 Using RHR-1 the force on wire 2 is away from wire 1
Using Newton’s Third Law, the force on wire 1 is away from wire 2
If the current in wire 2 is reversed, the direction of the forces is reversed

53. Magnetic Field Loop of Wire
Field at center of loop
N is number of coils in loop
R is the radius of the loop

54. Loop of Wire acts like Bar Magnet
Current-carrying loop acts like a bar magnet

55. Two Loop of Wire acts like Repel/Attract Bar Magnets
When the currents are in the same direction the loops attract
When the currents are in opposite directions the loops repel
Used RHR-1

56. Magnetic Field Long Solenoid
Field inside of solenoid
N is number of coils in loop

57. Ampere’s Law Constant magnetic field
Dl is a small segment of length along a closed path of arbitrary shape round the current
B|| is the component of the magnetic field parallel to Dl,
I is the net current passing through the surface bounded by the path
m0 is the permeability of free space
Symbol S indicates that the sum of all terms must be taken around the closed path

58. Problem 7 - 1
Use Ampere’s law to obtain the magnetic field produced by the current in an infinitely long, straight wire
Along the circular path the magnetic field is parallel to Dl and has constant magnitude

59. Problem 7 - 2