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Lecture 13-1
Fundamental forces in nature
• The strong interaction is very strong, but very shortranged. It acts only over ranges of order 10-13
centimeters and is responsible for holding the nuclei
of atoms together. It is basically attractive, but can be
effectively repulsive in some circumstances.
• The weak force is responsible for radioactive decay
and neutrino interactions. It has a very short range
and, as its name indicates, it is very weak.
• The gravitational force is weak,
• Electromagnetic forces:
– Electric forces
– Magnetic forces
Lecture 13-2
Magnetic Field
Permanent magnets: rocks from Magnesia, compass needle, bar magnet, …
• No net charge – no interactions with stationary charges
• Interactions - among themselves, N-S poles of the earth, with
materials such as iron, nickle, tapes, disks, …
moving charges
magnetism
action at distance like E
magnetic field
Define B by interaction with a
moving charge q
Lecture 13-3
Magnetic Field Lines
• Bar magnet ... two poles: N and S
Like poles repel; Unlike poles attract.
• Magnetic Field lines: (defined from the direction and
density of B similarly to the electric field lines are from E)
 B FB
 No sources
or sinks
From North to South outside
electric dipole
Lecture 13-4
More Permanent Magnets and Magnetic Field Lines
Lecture 13-5
Magnetic Monopoles
• Does there exist magnetic charge, just like electric charge? An entity which
carried such magnetic charge would be called a magnetic monopole (having
+ or - magnetic charge).
•
How can you isolate this magnetic charge? Try cutting a bar magnet in half.
• In fact no attempt has been successful in finding magnetic monopoles in nature.
Lecture 13-6
Magnetic Field B
• Magnetic force acting on a moving charge q depends on q, v.
Vary q and v in the presence of a given magnetic field
and measure magnetic force F on the charge. Find:
F v
F varies sinusoidally as
F  qv
direction of v is changed
F  qv  B
This defines B.
(q>0)
direction by Right Hand
Rule. B is a vector field
F  v, B F  qvB sin 
F
N
N



 T (tesla )
 B 
 qv  C  m / s A  m
1 T = 104 gauss (earth magnetic
field at surface is about 0.5 gauss)
vB
If q<0
Lecture 13-7
Magnetic Force on a Current
A
• Consider a current-carrying wire in the
presence of a magnetic field B.
• There will be a force on each of the charges
moving in the wire. What will be the total force
dF on a length dl of the wire?
• Suppose current is made up of n charges/volume
each carrying charge q < 0 and moving with
velocity v through a wire of cross-section A.
• Force on each charge =
• Total force =
• Current =
qv  B
dF  n A(dl ) qv  B
I  n Av q
For a straight length of wire L carrying a current I,
the force on it is:
dF  Idl  B
F  IL  B
Lecture 13-8
Lorentz Force
• The force F on a charge q moving with velocity v through a region of
space with electric field E and magnetic field B is given by:
F  qE  qv  B
B
x x x x x x
r
x x x x x x
v
x x x x x x
F q
m
Fm v  0
d 2
v  2v a  0
dt
(with E=0)
B

r
r
r
v
   
q
Fm
Fm
B
v
q
Fm = 0
Magnetic force does no work
Magnetic force does not change
speed
http://canu.ucalgary.ca/map/content/force/elcrmagn/simulate/magnetic/applet.html
Lecture 13-9
Both B and E present
Fm  qvB up
Fe  qE down
E
v 
B
when balanced
velocity selector
No deflection when
E=3 kV/m, B=1.4 G
v0  3000 /1.4 104
 2.143 107 (m / s)
http://canu.ucalgary.ca/map/content/force/elcrmagn/simulate/exb_thomson/applet.html
Lecture 13-10
Thomson’s e/m Measurement
x1= 4 cm
No deflection when
E=3 kV/m, B=1.4 G
v0  3000 /1.4 104
 2.143 107 (m / s)
x2 = 30 cm
2
Turn off B, and deflects
14.7 mm.
y 
1 eE  x1  eE  x1   x2 
3
  
     14.7  10 ( m)
2 m  v0 
m  v0   v0 
Thomson’s e/m

14.7  103 ( m)   2.143  107 ( m / s) 
2
e
11


1
.76

10
( C / kg )
3
m 3  10 ( N / C )  0.04( m)  (0.5  0.04  0.3)(m)
Lecture 13-11
Charged Particle Entering  Uniform Magnetic Field B
v2
qvB  m
r
mv
r
 const.
qB
vB
Constant speed
circular motion
Mass spectrometer
Lecture 13-12
Charged Particle Entering  Uniform Magnetic Field B
qB
2 r 2 m
qB
  2 f 
m
f 
v

Cyclotron
frequency
 proportional to B
 proportional to q/m
 independent of v
T 
1 2 m

f
qB
Cyclotron
period
2
1 2 1  qBr 
mv  m 
  q V
2
2  m 
Mass spectrometer
m B 2r 2
 
q 2 V