1. Last time… RC circuits Magnetic fields Magnetic dipole torque
Tue. Oct. 21, 2008
Physics 208 Lecture 15

2. Exam 2 is Tuesday Oct. 28 5:30-7 pm, 2103 Ch (here)
Students w / scheduled academic conflict please stay after class TODAY to arrange alternate time.
Covers: all material since exam 2.
Bring: Calculator
One (double-sided) 8 1/2 x 11 note sheet
Exam review: Thursday, Oct. 23, in class
Tue. Oct. 21, 2008
Physics 208 Lecture 15

3. Magnets and magnetic fields
Magnetic dipole aligns with magnetic field
Due to torque
Tue. Oct. 21, 2008
Physics 208 Lecture 15

4. Definition of Magnetic Field
Defined electric field based on electric force on a charged particle.
Is there a magnetic force on charged particle?
Observation:
Magnetic field as no effect on stationary charged particle
Tue. Oct. 21, 2008
Physics 208 Lecture 15

5. Magnetic force on moving charged particleS
Empirical facts: a) magnitude: µ to velocity of q
b) direction: ^ to direction of q q F v
mag
Tue. Oct. 21, 2008
Physics 208 Lecture 15

6. Magnetic force on electric charges
Effect of uniform B-field on charged particle
Charged particle not moving
no effect
Charged particle is moving:
force exerted perpendicular to both field and velocity
Tue. Oct. 21, 2008
Physics 208 Lecture 15

7. Magnetic force on charged particle
Magnitude of force is proportional to
Charge of particle, q
Speed of particle, v
Strength of magnet field, B
sin(), =angle between and
Direction of force is perpendicular to both and
vector ‘cross product’
Tue. Oct. 21, 2008
Physics 208 Lecture 15

8. FB on a Charge Moving in a Magnetic Field, Formula
FB = q v x B
FB is the magnetic force
q is the charge
v is the velocity of the moving charge
B is the magnetic field
SI unit of magnetic field: tesla (T)
CGS unit: gauss (G): 1 T = 104 G (Earth surface 0.5 G)
Tue. Oct. 21, 2008
Physics 208 Lecture 15

9. Quick Quiz
The three charges below have equal charge and speed, but are traveling in different directions in a uniform magnetic field.
Which particle experiences the greatest magnetic force? B 1 2 3 1 2 3
All same
F = q v B sin(q)
Tue. Oct. 21, 2008
Physics 208 Lecture 15

10. Quick Quiz
The three charges below have equal charge and speed, but are traveling in different directions in a uniform magnetic field.
The force on all the particles is in the same direction. B 1 2 3
True
False
All forces are into page
Magnitude F = q v B sin(q)
Tue. Oct. 21, 2008
Physics 208 Lecture 15

11. Force on moving charged particle
intermediate
Tue. Oct. 21, 2008
Physics 208 Lecture 15

12. More About Magnetic Force
The magnetic force acts only a moving charged particle
The magnitude of the magnetic force on a charged particle is FB = |q| vB sin q
FB is zero when v and B are parallel or antiparallel
FB is a maximum when v and B are perpendicular
The magnetic force NEVER does work on the particle.
Magnetic force perpendicular to the particle displacement
B field can alter direction of velocity, but not the speed or the kinetic energy
Tue. Oct. 21, 2008
Physics 208 Lecture 15

13. More force examples Force from B-field on moving charged particle
x x x x x x v B q
® ® ® ® ® v B q
­ ­ ­ ­ ­ ­ ­ ­ v B q F F
F = 0
Units: 1 T (tesla) = 1 N / Am
1G (gauss) = 10-4 T
Tue. Oct. 21, 2008
Physics 208 Lecture 15

14. Direction of Magnet Force on Moving ChargesUp
Down
Right
Left
Zero
Velocity B Force
out of page right up
out of page left down
out of page up ?
Do this demo with crt and bar magnet. I usually say CRT has positive charge, because – sign in direction is tough.
Might find better drawing of hand here. B
Right Hand Rule v F
Thumb v, Fingers B, palm F
Tue. Oct. 21, 2008
Physics 208 Lecture 15

15. Magnetic Force on a Current
Force on each charge
Force on length of wire
Force on straight section of wire, length L
Current N
Magnetic force S
Magnetic field
Tue. Oct. 21, 2008
Physics 208 Lecture 15

16. ‘Homopolar’ motor Why does the motor turn?
Electric Coulomb force pushes on magnet
Magnetic field pushes on current from battery
Current from battery heats the magnet
Current through wire produces magnetic field
Tue. Oct. 21, 2008
Physics 208 Lecture 15

17. Surprise! Electric current produces magnetic field
Current (flow of electric charges ) in wire produces magnetic field.
That magnetic field aligns compass needle
Current
Magnetic field
Tue. Oct. 21, 2008
Physics 208 Lecture 15

18. Magnetic field from a current
Iron filings align with magnetic field lines
Magnetic field loops around the current.
Tue. Oct. 21, 2008
Physics 208 Lecture 15

19. Magnetic field from long straight wire: Directiony
What direction is the magnetic field from an infinitely-long straight wire? x I
= permeability of free space
r = distance from wire
Tue. Oct. 21, 2008
Physics 208 Lecture 15

20. Magnetic field from loop of current
Tue. Oct. 21, 2008
Physics 208 Lecture 15

21. Quick Quiz L x y I
A current I flows in a square loop of wire with side length L.
A constant B field points in the -z direction, perpendicular to the plane of the loop.
What is the net force on the wire loop?
4LB
2LB LB
Tue. Oct. 21, 2008
Physics 208 Lecture 15

22. Torque on a current loopF
x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x B i
Consider loop in magnetic field as on right. Zero net force F
Force on right path cancels f orce on left path. (F = IBL)
Force on top path cancels force on bottom path (F = IBL) F B x . F
If plane of loop is not ^ to field, there will be a non-zero torque on the loop!
Tue. Oct. 21, 2008
Physics 208 Lecture 15

23. Torque on current loop Þ Þ since: A = wL = area of loop
Tue. Oct. 21, 2008
Physics 208 Lecture 15

24. Current loops & magnetic dipoles
Current loop produces magnetic dipole field.
Magnetic dipole moment:
Area of loop
current
magnitude
direction
Effect of uniform magnetic field
Magnetic field exerts torque Torque rotates loop to align with
Tue. Oct. 21, 2008
Physics 208 Lecture 15