1. Magnetic field
Chapter 28

2. Magnetism
Refrigerators are attracted to magnets!
Magnetism

3. Where is Magnetism Used??
Motors
Navigation – Compass
Magnetic Tapes
Music, Data
Television
Beam deflection Coil
Magnetic Resonance Imaging (MRI)
High Energy Physics Research
Magnetism

4. Cathode
Anode
(28 – 8)
Magnetism

5. Consider a Permanent Magnet
The magnetic Field B goes from North to South.
Magnetism

6. Units
Magnetism

7. Typical Representation
Magnetism

8. A Look at the Physics q If the charge is moving, there
There is NO force on
a charge placed into a
magnetic field if the
charge is NOT moving. q
There is no force if the charge
moves parallel to the field. q
If the charge is moving, there
is a force on the charge,
perpendicular to both v and B.
F = q v x B
Magnetism

9. The Lorentz Force This can be summarized as: F or: v q m B
q is the angle between B and V
Magnetism

10. Nicer Picture
Magnetism

11. The Wire in More Detail Assume all electrons are moving
with the same velocity vd. L
B out of plane of the paper
Magnetism

12. (28 – 12) . i
Magnetism

13. Current Loop
What is force
on the ends??
Loop will tend to rotate due to the torque the field applies to the loop.
Magnetism

14. Magnetic Force on a Current LoopS
F=BIL q L F B
Magnetism 63 41 66

15. Magnetic Force on a Current Loop
Simplified view:
F=BIL q L d I
Magnetism
F=BIL 63 43 66

16. Magnetic Force on a Current Loop Torque & Electric Motor
Simplified view:
F=BIL q L d I
Magnetism
F=BIL 63 45 66

17. Magnetic Force on a Current Loop Torque & Electric Motor
F=BIL d L q
for a current loop
Magnetism

18. C
Top view
Side view
(28 – 13)
Magnetism

19. Magnetic Force on a Current Loop Torque & Magnetic Dipole
By analogy with electric dipoles, for which:
The expression,
implies that a current loop acts as a magnetic dipole!
Here is the magnetic dipole moment,
and
(Torque on a
current loop)
Magnetism 63 47 66

20. Dipole Moment Definition
Define the magnetic
dipole moment of
the coil m as:
=NiA
t=m x B
We can convert this
to a vector with A
as defined as being
normal to the area as
in the previous slide.
Magnetism

21. Magnetism
(28 – 14)

22. L R
Magnetism
(28 – 15)

23. Motion of a charged particle in a magnetic Field
Magnetism

24. Trajectory of Charged Particles in a Magnetic Field
(B field points into plane of paper.) v B F B v F
Magnetism

25. Trajectory of Charged Particles in a Magnetic Field
(B field points into plane of paper.) v B B v F F
Magnetic Force is a centripetal force
Magnetism

26. Review of Rotational Motion s
 = s / r  s =  r  ds/dt = d/dt r  v =  r
 = angle,  = angular speed,  = angular acceleration  at ar
at = r  tangential acceleration
ar = v2 / r radial acceleration
The radial acceleration changes the direction of motion,
while the tangential acceleration changes the speed.
Uniform Circular Motion
 = constant  v and ar constant but direction changes
ar = v2/r = 2 r
F = mar = mv2/r = m2r
KE = ½ mv2 = ½ mw2r2 v  ar
Magnetism

27. Radius of a Charged Particle Orbit in a Magnetic Field
Centripetal Magnetic
Force Force = v B F r
Magnetism

28. Cyclotron Frequency V cancels ! B The time taken to complete one v v B F r
The time taken to complete one
orbit is:
V cancels !
Magnetism

29. Mass Spectrometer
Smaller Mass
Magnetism

30. Magnetism

31. An Example
A beam of electrons whose kinetic energy is K emerges from a thin-foil “window” at the end of an accelerator tube. There is a metal plate a distance d from this window and perpendicular to the direction of the emerging beam. Show that we can prevent the beam from hitting the plate if we apply a uniform magnetic field B  such that
Magnetism

32. Problem Continued r
Magnetism

33. #14 Chapter 28
 A metal strip 6.50 cm long, cm wide, and mm thick moves with constant velocity through a uniform magnetic field B= 1.20mTdirected perpendicular to the strip, as shown in the Figure. A potential difference of 3.90 ηV is measured between points x and y across the strip. Calculate the speed v.
FIGURE 28-37   
Problem 14.
Magnetism

34. 21.  (a) Find the frequency of revolution of an electron with an energy of 100 eV in a uniform magnetic field of magnitude 35.0 µT . (b) Calculate the radius of the path of this electron if its velocity is perpendicular to the magnetic field.
Magnetism

35. 39.  A 13.0 g wire of length L = 62.0 cm is suspended by a pair of flexible leads in a uniform magnetic field of magnitude T. What are the (a) magnitude and (b) direction (left or right) of the current required to remove the tension in the supporting leads?
Magnetism