12 Lecture 1/15
Fundamental Forces in Nature
Strong Interaction
very strong, but very short-ranged acts only over ranges of order 10-13 centimeters responsible for holding the nuclei of atoms together is basically attractive, but can be effectively repulsive in some circumstances.
Weak Force
responsible for radioactive decay and neutrino interactions has a very short range and, as its name indicates, is very weak
Gravitational Force
is weak
Electromagnetic Forces
Electric Forces Magnetic Forces
Lecture 12 2/15
Magnetic Field
Permanent magnets: rocks from Magnesia, compass needle, bar magnet, etc..
No net charge no interactions with stationary charges Interactions - among themselves, N-S poles of the earth, with materials such as iron, nickel, tapes, disks, etc.., moving charges magnetism action at distance like E field
magnetic field
Define B by interaction with a moving charge q
Lecture 12 3/15
Magnetic Field Lines
Bar magnet
two poles: North (N) and South (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
bar magnet
But different from E field lines...
B and FB are perpendicular while E and FE are in same direction B field lines do not begin or end while E field lines begin on positive charges and end on negative charges
magnetic field lines point from North to South electric dipole
Lecture 12 4/15
More Permanent Magnets and Magnetic Field Lines
Lecture 12 5/15
Magnetic Monopoles
Does there exist a magnetic charge, just like electric charge?
If so it would be called a magnetic monopole and carry a positive or negative magnetic charge (N or S pole)
How can you isolate a single magnetic charge?
Try cutting a bar magnet in half which can be modeled as
No attempt has been successful in finding magnetic monopoles in nature
Lecture 12 6/15
Magnetic Field B
Magnetic force (FB) acting on a moving charge depends on the magnitude of the charge (q) and the velocity (v) of the charge
Vary q and v in the presence of a magnetic field (B) and measure magnetic force (FB) on the charge Experimentally, we find that F varies sinusoidally as F v and F q v direction of v is changed
(q>0)
F
qv B
[F ] [q][v]
Magnetic field (B) is a vector and direction is given by Right Hand Rule
(q<0)
units of B is the tesla (T), 1 tesla (T) = 104 gauss (G)
[ B]
N C m/s
N A m
T (tesla)
Earth's magnetic field at surface is about 0.5 gauss (G)
Lecture 12 7/15
Magnetic Force on a Current
A
Consider a current-carrying wire in the presence of a magnetic field (B)
There is a force on each of the charges moving in the wire What is the total force dF on a length dl of the wire?
Suppose that the current
has n charges/volume each carrying charge q<0 and moving with velocity v through a wire of cross-section A
Force on each Fi charge: q v B Total force: dF ( n A dl ) v B Current: I n A v q
dF
I dl B
For a straight wire of length (L) carrying current (I), the force is
F
IL B
Lecture 12 8/15
Quiz Question 1
A current I flows in a wire that is oriented as shown. Which of the vectors represent the magnetic field that results in a maximum force on the wire?
I
Lecture 12 9/15
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
q E qv B
v
Fm q
x x x x x x
B x x x x x x v
x x x x x x
B
B
v q Fm = 0
F d)
Fm v 0 d 2 (v ) dt
Fm
q
Magnetic force (Fm) does no work! (W
2v a
0
Magnetic force (Fm) does not change speed!
http://canu.ucalgary.ca/map/content/force/elcrmagn/simulate/magnetic/applet.html
Lecture 12 10/15
Both B Field and E Field Present
What forces are acting on charge (q)?
Fe
Fm
When the forces are equal,
qE
qv B
down up
Fe qE
Fm qvB E v B
Only particles with a certain velocity pass through
If E = 3 kV/m and 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 12 11/15
Thomson's e/m Measurement
x1 = 4 cm
No deflection when E = 3 kV/m and B = 1.4 G,
v0
x2 = 30 cm Turn off B field and deflects particles y = 14.7 mm
y 1 e E x1 2 m v0
2
v0
3000 1.4 10 4 2.143 107 m/s
x2 v0
e E x1 m v0
14.7 10 3 m
Thomson's electron/mass ratio
e m y v0 E x1 (0.5 x1
2
x2 )
(14.7 10 3 m)(2.143 107 m/s) 2 (3 103 N/C) (0.04 m) (0.5 0.04 m 0.3 m)
1.76 1011 C/kg
Lecture 12 12/15
Charged Particles Entering Magnetic Field
v B
Particles travel perpendicular to magnetic field (B) In region with magnetic field (B),
Fnet
ma
FB
qv B
FB
q v B sin
ma
ma
Solve for the radius:
v2 qvB m r
constant speed and circular motion
r
mv qB
v
+q
F
Lecture 12 13/15
Charged Particles Entering Magnetic Field
v
y z
F
+q
If initial velocity (v) has no z-component, charge (q) x travels in a circle mv r qB
What is the period of oscillation? 1 2 2 r T ( 2 f) f v
cyclotron period cyclotron frequency
T
2 m qB
f
v 2 r
qB 2 m
2
Mass Spectrometer
In mass spectrometer, 1 kinetic energy equals m v2 potential energy loss 2
1 qBr m 2 m
q V
m q
B 2r 2 2 V
Lecture 12 14/15
Quiz Question 2
A positively charged particle is moving northward in a magnetic field. The magnetic force on the particle is toward the northeast. What is the direction of the magnetic field?
a) b) c) d) e) up northeast southwest down This situation cannot exist.
Lecture 12 15/15
Quiz Question 3
The left diagram shows a force F on a negatively charged particle moving a magnetic field B. Using the arrows in the right diagram, what is the direction of the velocity of the particle?